THE  FIRST  BOOK  OF  BOTANY. 


YOU  MANS’S  BOTANY. 


j 

Designed  to  cultivate  the  Observing  Powers  of  Children. 

Ft  118 


By  Eliza  A.  Youmans. 

iimo.  183  pages.  85  cents. 


In  the  use  of  this  book  there  are  no  lessons  to  “commit  and 
recite.”  The  pupil  commences  with  actual  specimens  of  plants 
which  every  one  is  able  to  collect,  and  learns  to  look  with  his 
own  eyes  and  think  with  his  own  mind.  Children  can  begin  to 
study  plants  successfully  by  this  method  as  soon  as  they  can 
write,  and  any  teacher,  without  previous  knowledge  of  the  subject, 
can  conduct  them  through  the  exercises  without  difficulty. 

Miss  Youmans  claims  that  Botany  may  be  made  to  do  for  the 
observing  faculties  what  mathematics  does  for  the  reasoning 
faculty,  and,  in  preparing  a book  by  which  this  work  may  be 
commenced,  she  has  met  the  profoundest  need  of  popular  educa- 
tion. 


D.  APPLETON  & CO.,  Publishers, 

S49  & 55 1 Broadway,  New  York. 


DUKE 

UNIVERSITY 

LIBRARY 


Gift  of 


H&ib&nt  C.  M osiAd,  II 


Digitized  by  the  Internet  Archive 
in  2016 


https://archive.org/details/logic01jevo_0 


LOCKYER’S  ASTRONOMY, 


ELEMENTS  OF  ASTRONOMY : 

Accompanied  with  numerous ' Illustrations,  a Colored  Repre- 
sentation of  the  Solar,  Stellar,  and  Nebular  Spectra, 
and  Celestial  Charts  of  the  Northern 
and  the  Southern  Hemisphere. 

By  J.  Norman  Lockyer. 

American  edition , revised  and  specially  adapted  to  the  Schools 
of  the  United  States. 

12 mo.  312  pages.  Price , $1.50. 

The  volume  is  as  practical  as  possible.  To  aid  the  student 
in  identifying  the  stars  and  constellations,  the  fine  Celestial 
Charts  of  Arago,  which  answer  all  the  purposes  of  a costly  Atlas 
of  the  Heavens,  are  appended  to  the  work — this  being  the  only 
text-book,  as  far  as  the  Publishers  are  aware,  that  possesses  this 
great  advantage.  Directions  are  given  for  finding  the  most  in- 
teresting objects  in  the  heavens  at  certain  hours  on  different 
evenings  throughout  the  year.  Every  device  is  used  to  make 
the  study  interesting;  and  the  Publishers  feel  assured  that 
teachers  who  once  try  this  book  will  be  unwilling  to  exchange 
it  for  any  other. 

D.  APPLETON  & CO.,  Publishers, 

549  & 55i  Broadway,  New  York. 


VvV- 


SCIENCE  PRIMERS,  edited  by 

Professors  Huxley,  Roscoe,  and 
Balfour  Stewart. 


LOGIC. 


Samce  llrirntrs 


LOGIC 

n . 


BY 

W.  STANLEY  JEVONS,  M.A.,  LL.D.,  F.R.S., 

PROFESSOR  OF  POLITICAL  ECONOMY  IN  UNIVERSITY  COLLEGE,  LONDON. 


WITH  ILLUSTRATIONS. 


NEW  YORK : 

D.  APPLETON  AND  COMPANY, 

549  and  551  Broadway. 


140 

•w*  ^ ) co 

I O — ? / 

I O I o 


CONTENTS. 


SECT.  PACE 

I. — Introduction 7 

II. — How  we  Commonly  Reason  .....  9 

III.  — What  is  Deductive  Reasoning?  ...  12 

IV.  — The  Different  Kinds  of  Terms  or 

Names 15 

V. — The  Full  Meaning  of  Terms 20 

VI.  — The  Correct  Use  of  Words 22 

VII.  — How  and  Why  we  Classify  Things  . . 27 

VIII. — Propositions 37 

IX. — How  to  Change  Propositions  ....  47 

X. — The  Syllogism 53 

XI. — The  Rules  of  the  Syllogism 56 

XII. — Hypothetical  Syllogisms 69 

XIII.  — Other  Kinds  of  Arguments 71 

XIV.  — The  Great  Rule  of  Inference  ....  73 

XV. — Inductive  Reasoning 76 

XVI. — Inductive  Reasoning  in  Ordinary  Life  . 85 

XVII.— Observation  and  Experiment  ....  89 


vi  CONTENTS. 

SECT.  PAGE 

XVIII. — Antecedents  and  Causes  of  Events  . . 92 

XIX. — Discovery  of  Agreements 95 

XX. — Things  which  Vary  in  Quantity  . . - . 97 

XXI.— Things  which  Vary  Periodically  ...  99 

XXII. —Reasoning  from  Experiments  ....  102 

XXIII. — How  and  When  to  Generalize  . . . . 104 

XXIV. — Reasoning  by  Analogy .107 

XXV. — Fallacies 112 

XXVI. — Fallacies  of  Ambiguity 114 

XXVII. — Fallacies  in  Inductive  Reasoning  . . 122 


SCIENCE  PRIMERS. 


LOGIC. 

I.— INTRODUCTION. 

i.  Monsieur  Jourdain,  an  amusing  person  in  one 
of  Moliere’s  plays,  expressed  much  surprise  on 
learning  that  he  had  been  talking  prose  for  more  than 
forty  years  without  knowing  it.  Ninety-nine  people 
out  of  a hundred  .might  be  equally  surprised  on  hear- 
ing that  they  had  long  been  converting  propositions, 
syllogizing,  falling  into  paralogisms,  framing  hypo- 
theses and  making  classifications  with  genera  and 
species. 

If  asked  whether  they  were  logicians,  they  would 
probably  answer,  No!  They  would  be  partly  right; 
for  I believe  that  a large  number  even  of  educated 
persons  have  no  clear  idea  what  logic  is.  Yet,  in  a 
certain  way,  every  one  must  have  been  a logician  since 
he  began  to  speak. 

It  may  be  asked  : — If  we  cannot  help  being 
logicians,  why  do  we  need  logic  books  at  all? 

The  answer  is  that  thsre  are  logicians  and  logicians. 
All  people  are  logicians  in  some  manner  or  degree ; 
but  unfortunately  many  people  are  bad  ones,  and 
suffer  harm  in  consequence.  It  is  just  the  same  in 
other  matters.  Even  if  we  do  not  know  the  meaning 


8 


PRIMER  OF  LOGIC. 


[i. 


of  the  name,  we  are  all  athletes  in  some  manner  or 
degree.  No  one  can  climb  a tree  or  get  over  a gate 
without  being  more  or  less  an  athlete.  Nevertheless, 
he  who  wishes  to  do  these  actions  really  well,  to  have 
a strong  muscular  frame,  and  thereby  to  secure  good 
health  and  personal  safety,  as  far  as  possible,  should 
learn  athletic  exercises  under  a skilful  teacher. 

2.  To  be  a good  logician  is,  however,  far  more 
valuable  than  to  be  a good  athlete  ; because,  logic 
teaches  us  to  reason  well,  and  reasoning 
gives  us  knowledge,  and  knowledge,  as  Lord 
Bacon  said,  is  power.  As  athletes  men  cannot 
for  a moment  compare  with  horses  or  tigers  or 
monkeys.  Yet,  with  the  power  of  knowledge,  men 
tame  horses  and  shoot  tigers  and  despise  monkeys. 
The  weakest  framework  with  the  most  logical  mind 
will  conquer  in  the  end,  because  it  is  able  to  foresee 
the  future,  to  calculate  the  results  of  actions,  to  avoid 
mistakes  which  might  be  fatal,  and  to  discover  the 
means  of  doing  things  which  seemed  impossible.  If 
such  little  creatures  as  ants  had  better  brains  than 
men,  they  would  either  destroy  men  or  make  them 
into  slaves. 

3.  It  is  true  that  we  cannot  use  our  eyes  or  ears 
without  getting  some  kind  of  knowledge,  and  the 
brute  animals  can  do  the  same.  But  what  gives 
power  is  the  deeper  knowledge  called 
Science.  People  may  see,  and  hear,  and  feel  all 
their  lives  without  really  learning  the  nature  of  things 
they  see.  But  reason  is  the  mind’s  eye,  and  enables 
us  to  see  why  things  are,  and  when  and  how  events 
may  be  made  to  happen  or  not  to  happen.  The  logi- 
cian endeavours  to  learn  exactly  what  this  reason  is 
which  makes  the  power  of  men.  We  all,  as  I have 
said,  must  reason  well  or  ill,  but  logic  is  the  science  of 
reasoning  and  enables  us  to  distinguish  between  the 
good  reasoning  which  leads  to  truth,  and  the  bad 


II.] 


REASONING. 


9 


reasoning  which  every  day  betrays  people  into  error 
and  misfortune. 


II.— HOW  WE  COMMONLY  REASON. 


4.  The  common  way  in  which  we  reason  is  to  ex- 
pect that  things  will  happen  as  they  have  happened 
before  in  like  circumstances.  Seeing  a bright  flash  of 
lightning,  I expect  thunder  to  follow,  because  it  has 
followed  bright  flashes  of  lightning  in  previous  cases. 
When  a bright  yellow  round  fruit  is  offered  to  me  I 
believe  it  to  be  an  orange  and  eat  it  without  hesita- 
tion, because  fruit  of  exactly  the  same  appearance 
had  been  eaten  before  without  harm.  The  gold  of 
Australia  was  discovered  by  this  simple  mode  of 
reasoning.  A man  named  Hargreaves  remarked  that 
the  mountains  of  New  South  Wales  were  like  those 
of  California,  where  he  had  been  digging  gold,  and  he 
reasoned  that  being  like  in  some  respects,  they  ought 
to  be  like  in  other  respects,  and  should  contain  gold. 
On  making  some  trials  he  found  that  he  was  correct. 

5.  But  in  this  simple  way  of  reasoning  from  like  to 
like  we  may  often  deceive  ourselves.  When  the  things 
which  we  believe  to  be  like  each  other  are  really  so, 
no  harm  is  done ; but  things  which  seem  to  be  like 
may  be  different : two  kinds  of  fungus  or  two  kinds 
of  fruit  may  so  closely  resemble  each  other  that  I 
may  not  notice  the  difference ; yet  one  kind  may  prove 
to  be  wholesome  to  eat  and  the  other  poisonous. 
It  is  even  possible  that  what  looks  exactly  like  an 
orange  might  be  some  new  sort  of  fruit,  and  not  an 
orange  at  all. 

People  are  so  accustomed  to  use  blankets  to  make 
themselves  warm  that  they  are  surprised  to  see 
blankets  used  to  keep  ice  cold,  and  to  prevent  it  from 
melting.  Expecting  that  the  same  thing  will  have  the 


10 


PRIMER  OF  J.OGIC. 


[ii. 


same  effect,  they  think  that  a blanket  must  make  ice 
warm.  But  this  would  not  really  be  a similar  effect. 
What  a blanket  always  does  is  to  prevent  heat  passing 
from  one  side  to  the  other.  Thus  it  keeps  the  heat 
of  the  body  from  passing  into  the  colder  air  around, 
and  it  keeps  the  heat  of  the  air  from  passing  into  the 
colder  ice.  Housemaids,  in  trying  to  make  a fire 
burn,  sometimes  reason  badly.  They  stick  the  poker 
among  the  coals  and  leave  it  there,  seeming  to  have  a 
belief  that  the  mere  presence  of  the  poker  helps  the 
fire  to  burn,  because  on  some  previous  occasions  the 
fire  had  burnt  better  when  the  poker  was  in  it.  They 
do  not  observe  that-  the  poker  is  only  useful  when  so 
placed  as  to  raise  the  coals  and  allow  the  air  to  enter 
freely. 

6.  The  truth  is  that  only  when  things  really  are 
alike  can  we  expect  them  to  behave  alike.  The  same 
causes  have  the  same  effects  ; but  the  difficulty  is  to 
know  when  the  causes  are  the  same.  To  ascertain 
this  requires  more  careful  reasoning  than  we  com- 
monly use.  We  need  to  discover  what  things  go  with 
other  things  always  and  everywhere  as  far  as  we  can 
observe.  We  have  to  find  out  what  are  called  the 
general  laws  showing  what  things  will  hap- 
pen under  given  circumstances.  A fire  some- 
times burns  and  sometimes  does  not  burn.  Then  the 
circumstances  must  be  different ; for  a fire  has  no 
will ; and  if  one  fire  be  laid  and  lighted  exactly  like 
another,  it  ought  to  burn  like  it.  We  must  find  out 
what  things  always  favour  the  burning,  such  as  the 
presence  of  abundant  air,  and  the  absence  of  moisture, 
and  of  any  body  which  can  carry  much  heat  away. 
We  shall  thus  learn  that  a cold  poker  put  into  a fire 
in  one  way  will  do  more  harm  than  good,  by  carrying 
away  heat ; but,  put  in  differently,  it  will  do  more 
good  than  harm,  by  admitting  air  and  quickening 
combustion. 


II.] 


REASONING. 


II 


7.  A general  law  of  nature  is  something 
which  is  true  of  many  objects,  and  science  is 
made  up  of  such  laws.  After  reflecting  a little, 
we  shall  see  that  logic  ought  to  teach  us  to  do  two 
different  things  with  respect  to  the  laws  of  nature, 
namely,  how  to  discover  them,  and  how  to  use  them 
when  discovered.  By  inductive  reasoning,  as  it 
is  called,  we  ascertain  what  is  true  of  many  different 
things.  Our  eyes,  and  ears,  and  other  senses  tell  us 
what  happens  around  us,  and  then  by  proper  reason- 
ing we  may  often  discover  the  laws  of  nature,  in 
consequence  of  which  they  happen.  Observing  that 
clouds,  rain,  snow,  hail,  dew,  mist,  and  fogs,  consist  of 
water,  which  seems  to  come  out  of  the  air,  we  may,  by 
a proper  course  of  inquiry,  discover  that  all  moist  air, 
when  cooled  in  a certain  degree,  produces  particles  of 
water.  We  find  that  there  is  something  the  same  in 
the  causes  of  all  these  things. 

8.  By  deductive  reasoning  we  do  just  the 
opposite,  and  from  any  law  of  nature  we  infer  what 
will  happen  in  consequence  of  it.  To  infer  is  to 
find  out  what  will  be  true  if  something  else 
is  true.  Knowing  that  moist  air  when  cooled  pro- 
duces particles  of  water,  I may  infer  that  an  iced 
bottle  of  wine  will  in  summer  become  covered  with  dew. 
Philosophers  have  discovered  by  induction  that  all 
bodies  tend  to  fall  towards  the  earth  like  stones  ; then 
by  deduction  I can  infer  that  the  moon  must  tend  to 
fall  towards  the  earth.  It  may  seem  as  if  all  the 
difficulty  of  reasoning  lies  in  discovering  laws  by  in- 
duction, and  that  we  must  certainly  learn  to  discover 
the  laws  before  we  learn  how  to  use  them.  The 
fact,  however,  is  that  we  cannot  possibly  understand 
inductive  reasoning  unless  we  previously  understand 
deductive  reasoning. 

9.  Before  we  can  be  said  to  know  properly  what  a 
law  of  nature  means,  we  must  be  a'de  to  see  what  it 


12 


PRIMER  OF  LOGIC. 


[m. 


leads  to,  that  is,  to  infer  its  consequences.  I cannot 
tell  whether  a law  is  true  or  not  unless  I see  whether 
it  agrees  with  what  happens  in  nature.  When  philo- 
sophers came  to  the  conclusion  that  all  material 
bodies  tend  to  fall  towards  the  earth,  they  ought  to 
hav'e  been  able  to  foresee  that  the  moon,  being  a 
material  body,  would  tend  to  fall  towards  the  earth, 
so  as  to  inquire  whether  this  was  true  or  not.  I 
shall  afterwards  show  more  fully  that  it  is  really  by 
the  use  of  deductive  reasoning  that  we  perform  in- 
ductive reasoning.  We  will  now  proceed  at  once  to 
consider  what  deductive  reasoning  consists  in. 

III. — WHAT  IS  DEDUCTIVE  REASONING? 

ro.  Let  us  take  a simple  case  of  reasoning,  an  argu- 
ment, as  it  is  often  called,  and  consider  in  what  way 
it  is  constructed.  When  we  see  a particular  kind  of 
white  and  pink  fungus,  and  pluck  it,  because  wre 
believe  it  to  be  a mushroom,  and  we  know  that  all 
mushrooms  are  good  to  eat,  we  certainly  reason  by 
an  argument,  which  may  be  thus  fully  stated  : — 

All  mushrooms  are  good  to  eat ; 

This  fungus  is  a mushroom  ; 

Therefore,  this  fungus  is  good  to  eat. 

Here  are  three  sentences  which  state  three  different 
facts ; but  when  we  know  the  two  first  facts,  we  learn 
or  gather  the  third  fact  from  the  other  two.  When  we 
thus  learn  one  fact  from  other  facts,  we  infer  or  reason, 
and  we  do  this  in  the  mind.  Reasoning  thus  enables  us 
to  ascertain  the  nature  of  a thing  without  actual  trial. 
If  we  always  needed  to  taste  a thing  before  we  could 
know  whether  it  was  good  to  eat  or  not,  cases  of 
poisoning  would  be  alarmingly  frequent.  But  the 
appearance  and  peculiarities  of  a mushroom  may  be 
safely  learned  by  the  eye  or  the  nose,  and  reasoning 


III.] 


REASONING. 


13 

upon  this  information  and  the  fact  already  well-known, 
that  mushrooms  are  good  to  eat,  we  arrive  without 
any  danger  or  trouble  at  the  conclusion  that  the 
particular  fungus  before  us  is  good  to  eat.  To 
reason,  then,  is  to  get  some  knowledge  from 
other  knowledge. 

11.  Let  us  now  examine  more  carefully  the  parts  of 
which  this  argument  about  mushrooms  is  made  up. 
There  are  three  sentences,  which  put  facts  before  us, 
and  are  therefore  called  Propositions.  The  first 
proposition  tells  us  that  “All  mushrooms  are  good 
to  eat,”  or,  -what  means  exactly  the  same,  “All  mush- 
rooms are  things  good  to  eat.”  This  proposition  has 
three  principal  parts.  There  are  two  descriptions  of 
things  compared  together,  namely,  “mushrooms”  and 
“things  good  to  eat.”  These  kinds  of  things  are 
mentioned,  of  course,  by  their  names,  and,  as  the 
name  mushroom  is  at  one  end  of  the  proposition, 
and  things  good  to  eat  at  the  other  end,  these  names 
are  called  the  terms,  or  ends  of  the  proposition. 
They  are  connected  together  by  the  little  verb  “ are,” 
which  is  called  the  copula  or  link.  There  remains, 
indeed,  the  little  adjective  “all,”  which  tells  us  how 
many  of  the  mushrooms  are  good  to  eat ; in  the  case 
of  other  things  'it  might  be  few,  or  many,  or  none. 
In  this  case  it  is  all,  and  we  may  call  this  the  sign 
of  quantity. 

The  other  propositions  are  made  up  nearly  in  the 
same  way.  Thus,  in  “This  fungus  is  a mushroom,”  we 
observe  two  terms,  namely,  “this  fungus,”  and  “mush- 
room,” which  are  connected  together  by  the  copula 
“ is.”  In  the  third  proposition,  which  we  drew  from  the 
other  two,  the  terms,  “ this  fungus  ” and  “ thing  good 
to  eat,”  are  found  over  again,  with  the  copula  “ is.” 
It  will  be  observed  that  each  term  is  used  twice  over 
in  the  argument ; “ this  fungus  ” occurs  in  the  second 
and  third  propositions  ; “ mushroom  ” in  the  first  and 
2 


*4 


PRIMER  OF  LOGIC. 


[iv. 


second ; and  “thing  good  to  eat”  in  the  first  and  third. 
We  learn  from  our  examination,  that  an  argument  of 
this  kind  consists  of  three  propositions  and  of  three 
terms,  and  that  each  proposition  is  made  by  joining 
two  terms.  When  we  join  terms  together  we 
make  a proposition  ; when  we  join  proposi- 
tions together  we  make  an  argument,  or 
piece  of  reasoning. 

12.  We  should  generally  get  nothing  but  nonsense 
if  we  were  to  put  together  any  terms  and  any  proposi- 
tions, and  to  suppose  that  we  were  reasoning.  To 
produce  a good  argument  we  must  be  careful  to  obey 
certain  rules,  which  it  is  the  purpose  of  Logic  to  make 
known.  But,  in  order  to  understand  the  matter 
perfectly,  we  ought  first  to  learn  exactly  what  a term 
is,  and  how  many  kinds  of  terms  there  may  be ; we 
have  next  to  learn  the  nature  of  a proposition,  and 
the  different  kinds  of  propositions.  Afterwards  we 
shall  learn  how  one  proposition  may  by  reasoning  be 
drawn  from  other  propositions  in  the  kind  of  argument 
called  the  syllogism.  Thus,  there  are  three  parts 
of  Deductive  Logic,  which  treat  of  Terms, 
Propositions,  and  Syllogisms.  Terms  and  pro- 
positions are,  indeed,  merely  the  tools  which  we  use 
in  reasoning : but  we  cannot  learn  a trade  unless  we 
begin  with  learning  the  use  of  the  tools  employed  in  it. 
Hence  we  shall  begin  by  considering  the  different 
kinds  of  terms  and  propositions  before  we  go  on 
to  the  syllogism. 

IV.— THE  DIFFERENT  KINDS  OF  TERMS  OR 
NAMES. 

13.  As  we  have  already  learnt,  terms  are  the 
names  of  the  things  which  we  compare  together  in 
a proposition.  Now  names  consist  of  what  the  gram- 
mar books  call  nouns,  and  a single  term  may  con- 


IV.] 


TERMS. 


15 


tain  any  number  of  nouns,  substantive  or  adjective. 
Sometimes  there  is  in  each  term  only  a single  noun. 
Thus  in  “ Diamonds  are  combustible,”  the  first  term 
is  the  single  substantive  “ diamonds  ” ; the  second 
term  is  the  single  adjective  “ combustible.”  But  a 
term  will  often  be  made  of  two  or  more  nouns  joined 
together  in  some  way.  The  proposition  “The  Queen 
of  England  is  the  Empress  of  India  ” contains  only 
two  terms,  but  each  of  them  is  composed  of  two 
nouns,  “ Queen  of  England  ” being  the  first  term, 
“ Empress  of  India,”  the  second.  “ The  library  of 
the  British  Museum  is  the  greatest  collection  of  books 
in  the  world.”  Here  is  a proposition  containing  fifteen 
words,  yet  it  has  only  two  terms  ; the  first  is  “ The 
library  of  the  British  Museum,”  in  which  we  see  two 
substantives,  one  adjective,  two  definite  articles  and 
one  preposition  ; the  second  is  “the  greatest  collection 
of  books  in  the  world,”  in  which  we  see  three  sub- 
stantives, one  adjective,  two  articles,  and  two  preposi- 
tions. A logical  term,  then,  may  consist  of  any 
number  of  nouns,  substantive  or  adjective,  with  the 
articles,  prepositions  and  conjunctions  required  to  join 
them  together;  still  it  is  only  one  term  if  it  points 
out,  or  makes  us  think  of  a single  object,  or  collection, 
or  class  of  objects.  But  there  are  several  different 
kinds  of  terms,  which  we  must  next  consider. 

14.  Sometimes  a term  points  out  only  a single 
person  or  thing,  as  “ The  Queen  of  England,”  “ The 
British  Museum,”  “ Pompey’s  Pillar.”  By  the  Queen  of 
England  we  mean  the  present  reigning  Queen  Victoria, 
and  there  is,  of  course,  only  one  Queen  Victoria. 
There  is  only  one  British  Museum,  and  one  single 
great  obelisk  called  Pompey’s  Pillar.  Hence  terms 
of  this  kind  are  called  singular  terms,  because  each 
term  is  the  name  only  of  a single  thing. 

15.  The  greater  number  of  terms  used  in  writing 
and  speaking  are,  however,  not  singular  but  general 


i6 


PRIMER  OF  LOGIC. 


[IV. 


terms.  They  are  the  names  of  things  of  which 
many  exist.  Thus  “ shilling  ” is  not  the  name  of  any 
one  single  thing,  like  “ Pompey’s  Pillar.”  There  are 
many  millions  of  things,  each  of  which  can  be  called  a 
shilling ; and  when  I say  that  “ all  shillings  are  made 
of  a mixture  of  silver  and  copper,”  I mean  to  state 
this  of  any  and  all  the  shillings.  In  the  same  way 
“ horse  ” is  the  name  of  any  one  of  millions  of  horses 
which  may  exist  in  the  world.  The  number  of  things 
denoted  by  a general  term  may  vary  from  two  or 
three  to  numbers  exceeding  anything  that  we  can 
conceive.  “ Present  King  of  Siam  ” is  the  general 
term  for  either  of  the  two  existing  kings  of  that 
country;  “House  of  Parliament”  is  the  general  name 
either  of  the  Lords  or  the  Commons.  “ Grain  of 
sand,”  is  the  name  of  any  one  of  many  billions,  or 
even  trillions  of  little  particles ; and  “ particle  of 
matter”  is  a still  wider  general  name;  for  all  sub- 
stances which  exist  in  the  universe  are  composed  of 
minute  particles  of  matter. 

16.  It  may  be  remarked,  indeed,  that,  as  even  a 
single  thing,  like  Pompey’s  Pillar,  is  made  up  of 
many  portions  of  matter,  the  name  of  the  whole  must 
be  the  name  of  all  the  parts.  The  continent  of  Asia 
is  made  up  of  many  plains,  lakes,  mountains  and 
rivers.  Polynesia  is  the  name  of  an  immense  number 
of  islands  scattered  about  the  Pacific  Ocean.  Never- 
theless, each  of  these  .things  is  a single  whole.  There 
are  not  two  Pompey’s  Pillars  in  existence,  nor  two 
Asias,  nor  two  Polynesias.  Hence  each  of  these  terms 
is  a singular  term,  not  a general  term,  and  a singular 
term  may  be  the  name  of  many  things,  provided  they 
are  all  put  together  into  one  single  group  or  collec- 
tion. Polynesia  is  the  name  not  of  any  one  island, 
but  of  a great  many  islands  in  the  Pacific  Ocean. 
Such  a term  is  called  a Collective  term,  because  it 
is  the  name  of  many  things  collected  into  one  whole. 


IV.] 


TERMS. 


17 


Library  is  the  collective  name  for  many  books  put 
together ; constellation,  of  many  stars ; crowd,  of 
many  people. 

77.  I have  said  that  a general  name  is  the  name  of 
many  things  ; but  then  it  is  the  name  of  any  one 
of  those  things  separately  from  the  others.  Thus 
“island”  is  the  name  of  any. one  of  the  thousands  of 
small  pieces  of  land  making  up  Polynesia.  Island, 
then,  is  a general  term  ; Polynesia  is  a collective  and 
singular  term.  The  British  Museum  Library  is  the 
name  of  a great  collection  of  books,  not  of  any  one 
of  those  books  ; it  is,  therefore,  a collective  term,  and 
is  also  singular.  There  are,  however,  a great  many 
collections  of  books  of  various  size  in  the  world, 
so  that  the  term  “ Library,”  though  it  is  collective 
as  regards  the  books  in  any  particular  library,  is 
yet  general,  because  it  is  the  name  of  any  such 
collection.  We  thus  see  that  the  same  term  may  be 
at  once  collective  and  singular,  or  collective  and 
general ; but  we  must  always  take  great  care 
to  avoid  confusing  collective  terms  with 
general  terms. 

18.  There  is  another  difference  between  terms 
which  it  is  not  so  easy  to  understand.  Many  terms 
are  the  names  of  solid  objeots,  which  we  can  touch 
or  move  about,  and  which  exist  by  themselves,  like  a 
half-crown,  a writing  slate,  or  a brick  house.  Such 
terms  are  called  Concrete  terms,  and  they  include 
most  names  which  may  be  put  in  the  plural ; thus  we 
may  speak  of  half-crowns,  brick  houses,  mountains, 
planets,  particles  of  matter,  and  so  on.  All  these  are 
concrete  terms. 

Abstract  terms,  on  the  contrary,  are  names,  not 
exactly  of  things,  but  of  qualities  which  belong  to 
things,  as  the  thickness  of  a half-crown,  the  colour  of 
a slate,  the  magnitude  of  a house,  the  elevation  of  a 
mountain.  We  cannot  separate  the  thickness  of  a 


iS 


PRIMER  OF  LOGIC. 


[IV. 


half-crown  from  the  half-crown,  as  we  can  separate 
one  half-crown  from  another.  Every  object  has  many 
qualities ; a half-crown,  besides  thickness,  has  weight, 
solidity,  colour,  ductility,  malleability,  fusibility,  con- 
ductibility,  and  many  other  qualities,  so  that  each  of 
these  terms  is  an  abstract  one.  Properly  speaking, 
an  abstract  term  cannot  be  put  into  the  plural.  We 
ought  not  to  speak  of  solidities,  ductilities,  fusibilities, 
these  being  perfectly  abstract  terms.  It  is  true  that 
we  often  speak  of  colours,  weights,  magnitudes ; but 
it  is  probable  that  we  then  make  the  terms  concrete. 
Altogether,  there  is  much  confusion  between  abstract 
and  concrete  terms,  and  the  difference  between  them 
is  not  well  understood.  It  will  be  sufficient  to  re- 
member that  a concrete  term  is  the  name  of  a 
thing ; an  abstract  term  is  the  name  of  a 
quality  of  a thing. 

1 9.  We  must  now  ascertain  the  difference  between 
positive  and  negative  terms.  As  a general  rule 
we  give  a name  to  a thing  because  it  has  a certain 
quality.  We  call  a house  “a  brick  house,”  because 
it  is  made  of  bricks  ; black-lead  is  so  called  because 
it  is  black,  and  looks  like  lead.  But  in  other  cases 
we  give  a name  to  a thing  for  the  opposite  reason, 
because  it  has  not  got  a certain  quality.  Thus  we 
call  a feat  impossible,  because  it  cannot  be  done ; 
a speech  is  unparliamentary  when  it  does  not  agree 
with  the  rules  of  parliamentary  debate  ; an  immense 
distance  means  a distance  which  has  not  been 
measured;  an  uneven  surface  is  one  not  possessing 
evenness ; unfiltered  water  is  water  which  has  not 
been  filtered.  All  these  are  negative  terms.  We  may 
usually  know  a negative  term  by  its  beginning  with 
one  of  the  little  syllables  un-,  in-,  a-,  an-,  non-,  or  by 
its  ending  with -less.  Thus  unfavourable,  indivisible, 
amorphous,  anonymous,  non-metallic,  useless,  are 
negative  terms.  But  there  are  also  many  terms  which 


IV.] 


TERMS. 


19 


may  be  said  to  serve  as  negative  terms,  although  they 
have  no  such  mark  at  the  beginning  or  end.  When  a 
piece  of  metal  can  be  hammered  out  into  a thin  plate 
we  call  it  malleable  ; when  it  cannot  be  so  hammered 
out,  it  might  be  called  immalleable ; but  this  word 
has  seldom  been  used,  and  we  generally  call  such-  a 
piece  of  metal  brittle.  Thus  “ brittle  ” serves  as  the 
negative  term  of  “ malleable.”  Similarly,  opaque  is 
the  negative  of  transparent,  false  of  true,  dry  of 
moist,  rough  of  smooth,  and  so  on.  When  we  are 
speaking  of  written  or  spoken  compositions,  verse  is 
the  negative  of  prose,  and  prose  the  negative  of  verse, 
unless,  indeed,  Monsieur  Jourdain  was  right  in  think- 
ing that  he  could  get  a love-letter  written  neither  in 
verse  nor  in  prose. 

20.  If  the  English  language  were  a perfect  one, 
every  term  ought  to  have  a negative  term  exactly  cor- 
responding to  it,  so  that  all  adjectives  and  nouns 
would  be  in  pairs.  Just  as  convenient  has  its  negative 
inconvenient;  metallic,  non-metallic;  logical,  illogical ; 
and  so  on  ; so  blue  should  have  its  negative  non-blue; 
literary,  non-literary  ; paper,  non-paper.  But  many  of 
these  negative  terms  would  be  seldom  or  never  used, 
and,  if  we  happen  to  want  them,  we  can  make  them 
for  the  occasion  by  putting  not-,  or  non-,  before  the 
positive  term.  Accordingly,  we  find  in  the  dictionary 
only  those  negative  terms  which  are  much  employed. 
When  we  are  speaking  in  England  of  those  belonging 
to  Christian  sects,  a Churchman  means  one  belonging 
to  the  Church  of  England.  Those  who,  being  Chris- 
tians, are  not  Churchmen,  are  called  Dissenters,  so 
that  the  term  Dissenter  serves  as  the  negative  of 
Churchman.  But  we  have  no  separate  names  for 
those  who  are  not-Wesleyans,  or  not-Methodists,  or 
not-Baptists. 

Sometimes  the  same  word  may  seem  to  have  two 
or  even  more  distinct  negatives.  There  is  much 


20 


PRIMER  OF  LOGIC. 


[v. 


difference  between  undressed  and  not-dressed,  that  is 
“ not  in  evening  dress.”  Both  seem  to  be  negatives 
of  “ dressed,”  but  this  is  because  the  word  has  two 
distinct  meanings. 

21.  Mistakes  frequently  arise  from  not  observing  the 
distinction  between  negative  terms  which  indicate  the 
complete  absence  of  some  quality,  and  comparative 
or  opposite  terms  which  only  mean  various  degrees  of 
the  property.  Thus  the  term  “ small  ” is  not  really 
the  negative  of  “ large,”  because  there  may  be  things 
which  are  neither  large  nor  small,  that  is,  are  of 
medium  size.  The  negative  of  large  is  not-large, 
which  includes  both  medium  and  small;  similarly,  the 
negative  of  small  is  not-small,  which  includes  both 
medium  and  large.  So  with  warm  and  cold,  light  and 
dark,  heavy  and  light ; these  are  not  pairs  of  positive 
and  negative  terms,  unless  by  cold  we  mean  the  entire 
absence  of  warmth,  by  dark  the  entire  absence  of  light, 
and  so  on,  as  we  seldom  do.  We  never  can  make 
anything  so  cold  that  it  contains  no  heat  at  all ; the 
question  is  altogether  one  of  degree.  Thus  the  word 
“ hot,”as  we  generally  use  it,  does  not  mean  “possessing 
heat,”  the  negative  of  which  would  be  “ not  possessing 
heat,”  but  “ possessing  more  than  medium  heat,” 
the  negative  of  which  is  “ not  possessing  more  than 
medium  heat,”  and  includes  both  things  which  are  of 
medium  temperature  and  those  which  would  be  called 
cold.  If  then  a person  denies  that  a thing  is  hot,  he 
ought  not  to  be  understood  as  asserting  that  it  is  cold, 
for  it  may  be  just  short  of  being  hot,  and  yet  not  cold. 


V.— THE  FULL  MEANING  OF  TERMS. 

22.  We  cannot  really  form  a clear  notion  of  what 
a concrete  term  means  unless  we  observe  that  there 
are  two  different  kinds  of  meanings,  namely,  the 

things  to  which  the  term  is  applied,  and  the 


V.] 


TERMS. 


21 


qualities  of  those  things  in  consequence  of 
which  it  is  applied.  When  I see  a large  peculiar- 
shaped iron  structure  floating  on  the  water  with  masts 
and  sails,  I call  it  a ship,  because  it  is  evidently 
adapted  to  sailing  and  conveying  goods  and  pas- 
sengers. Every  other  structure  having  the  same 
general  appearance  and  purpose  I also  call  ship,  and 
if  I were  asked  Why,  I should  have  to  answer  as 
best  I could,  that  every  large  vessel  made  to  move 
through  the  water  easily  and  convey  things  is  a ship. 
Whenever,  then,  I call  a thing  a ship  I must  mean 
that  it  has  these  peculiarities  ; it  is  these  circumstances 
which  make  it  a ship,  and  lead  me  to  use  the  name 
ship ; so  that  the  word  means  that  the  thing  to  which 
it  is  applied  is  made  to  move  easily  through  the  water, 
and  so  forth.  But,  on  the  other  hand,  the  name  ship 
is  the  name  of  the  thing,  and  there  are  a great  many 
particular  ships,  such  as  the  Great  Britain , the  Great 
Eastern , the  Challenger , the  Castalia , the  Minotaur , 
the  Vanguard. 

In  reality  every  ordinary  general  term  has  a double 
meaning : it  means  the  things  to  which  it  is  applied, 
for  instance,  the  particular  ships  named  : it  also  means 
in  a totally  different  way,  the  qualities  and  peculiarities 
implied  as  being  in  the  things.  Logicians  say  that 
the  number  of  things  to  which  a term  applies  is  the 
extension  of  the  term  ; while  the  number  of  quali- 
ties or  peculiarities  implied  is  the  intension. 

23.  When  we  compare  together  terms  which  are 
partly  different  and  partly  the  same,  we  shall  find 
that  they  have  various  degrees  of  extension  and  in- 
tension. Take,  for  instance,  the  term  “ship”  and 
compare  it  with  “steam-ship.”  There  are  evidently 
m^ny  more  ships  than  there  are  steam-ships,  because 
we  have  in  the  meaning  of  the  latter  term  to  exclude 
sailing  ships.  Hence  in  putting  steam  before  ship  we 
have  greatly  reduced  the  extension  of  the  term.  But 


22 


PRIMER  OF  LOGIC. 


[vr. 


we  have  increased  its  intension,  because  steam-ship 
means  all  that  ship  does,  and  more,  for  it  means 
that  the  ship  is  moved  by  steam  power.  Put  another 
word  before  it  and  compare  screw-steam-ship  with 
steam-ship,  and  we  find  we  have  again  reduced  the 
extension,  by  putting  out  of  sight  the  steam-ships  yet 
propelled  by  paddles  ; these  are  comparatively  few 
in  the  present  day,  so  that  we  have  not  made  any 
very  great  difference  ; but  we  have  nevertheless  in- 
creased the  intension  of  meaning  considerably,  because 
we  know  precisely  in  what  way  a thing  called  a screw- 
steam-ship  is  moved.  War-screw-steam-ship  is  a still 
narrower  term,  that  is,  has  much  less  extension, 
because  it  now  applies  only  to  those  ships  owned  by 
a government  for  war  purposes  ; but  this  makes  an 
addition  to  the  intension  or  the  circumstances  and 
qualities  implied.  British-war-screw-steam-ship  is  in 
like  manner  a still  narrower  term,  and  we  might  go  on 
further  specifying  that  it  is  iron  clad,  that  it  is  in 
commission,  is  in  the  Channel  Fleet.  We  have  thus 
narrowed  the  extension  so  much  that  there  may  only 
be  half-a-dozen  ships  to  which  our  description  will 
now  apply.  If  we  add  that  it  bears  the  Admiral’s 
flag,  this  removes  all  but  a single  ship,  so  that  the 
extension  is  reduced  to  the  least  possible.  At  the 
same  time  the  intension  becomes  very  great,  and  if 
we  happen  to  be  acquainted  with  the  ship,  and  to 
have  heard  much  about  it,  all  the  knowledge  which 
we  have  of  the  ship  is  suggested  by  the  name. 


VI.— THE  CORRECT  USE  OF  WORDS. 

24.  In  endeavouring  to  reason  correctly,  there  is 
nothing  more  necessary  than  to  use  words  with  care. 

The  meaning  of  a word  is  that  thing  which 
we  think  about  when  we  use  the  word,  and 


VI.] 


USE  OF  WORDS. 


23 


which  we  intend  other  people  to  think  about  when 
they  hear  it  pronounced,  or  see  it  written.  We  can 
hardly  think  at  all  without  the  proper  words  coming 
into  the  mind,  and  we  can  certainly  not  make  known 
to  other  people  our  thoughts  and  arguments  unless  we 
use  words.  Yet  there  is  no  more  common  source  of 
mistakes  and  bad  reasoning  than  the  confusion  which 
arises  between  the  different  meanings  of  the  same 
word. 

25.  Take  for  instance  the  word  “church.”  It 
may,  no  doubt,  be  said  to  mean  the  solid  building  of 
stone  or  brick,  to  which  people  go  to  worship,  and 
when  used  in  this  sense  there  can  seldom  be  any 
important  mistake.  But  it  is  also  common  to  speak 
of  the  Church  as  meaning  the  whole  body  of  people 
who  worship  in  a particular  manner,  and  have  the 
same  creed  and  ritual.  Thus  there  is  the  Church  of 
England,  the  Church  of  Rome,  the  Greek  Church, 
the  Free  Church  of  Scotland,  and  so  forth.  When 
we  say  a person  has  gone  over  to  the  Church  of 
Rome,  we  do  not  mean  that  he  has  gone  bodily  to 
Rome,  but  that  he  has  simply  changed  his  belief. 
Each  different  sect  too  speaks  of  the  Church  as  mean- 
ing their  own  Church,  so  that  two  people  arguing 
together  and  speaking  of  the  Church  may  mean  totally 
different  Churches. 

26.  There  is,  however,  a still  more  serious  confusion 
in  the  meanings  of  the  word,  because  the  bishops, 
clergy,  and  other  authorities  of  the  Church,  being 
the  most  prominent  members  of  it,  and  governing, 
representing,  and  expressing  the  opinions  of  the 
Church,  often  come  to  be  spoken  of  as  if  they  were 
the  Church.  Properly  speaking,  the  congregation 
who  attend  worship  have  as  much  right  to  be  con- 
sidered part  of  the  Church  as  the  clergy,  and  they 
have,  to  a certain  extent,  the  right  of  electing  officers, 
of  deciding  questions  about  the  building,  and  so  forth. 


24 


PRIMER  OF  LOGIC. 


[VI. 


But,  if  we  include  the  congregation,  how  are  we  to 
decide  who  shall  be  counted  as  proper  members  ? 
Not  everybody  who  goes  inside  a church  door  can  be 
called  a member  of  the  Church.  For  some  purposes 
we  should  include  only  regular  communicants;  for 
other  purposes  those  who  have  been  baptized,  and 
confirmed,  and  not  excommunicated  ; many  overlook 
the  confirmation,  and  there  may  be  persons  who, 
without  having  been  even  baptized,  consider  them- 
selves members  of  a Church,  because  they  have  re- 
gularly attended  worship,  and  have  subscribed  towards 
the  expenses.  Even  while  we  are  discussing  the 
word  “church,”  it  is  difficult  to  avoid  speaking  more 
in  reference  to  some  one  Church,  for  instance,  the 
Church  of  England,  than  to  other  Churches.  We 
must  remember  that  the  Wesleyan,  Baptist,  Roman 
Catholic,  and  many  other  Churches,  take  much  care 
to  ascertain  and  settle,  who  do,  and  who  do  not 
belong  to  their  particular  Churches. 

27.  In  many  cases  the  meanings  of  a word  are  so 
distinct  that  they  cannot  really  lead  us  into  more  than 
a momentary  misapprehension,  or  give  rise  to  a pun. 
A rake  may  be  either  a garden  implement,  or  a fast 
young  man ; a sole  may  be  a fish,  or  the  sole  of  the 
foot ; a bore  is  either  a tedious  person,  a hole  in  a 
cannon,  or  the  sudden  high  wave  which  runs  up  some 
rivers  when  the  tide  begins  to  rise ; diet  is  the  name 
of  what  we  eat  daily,  or  of  the  Parliament  which 
formerly  met  in  Germany  and  Poland ; ball  is  a 
round  object,  or  a dance.  In  some  cases  a word  is 
really  a different  word  in  each  of  two  or  three  mean- 
ings, and  comes  from  quite  different  words  in  other 
languages.  Thus,  bale  is  the  name  of  a bundle  or 
package  of  goods,  and  seems  to  be  derived  from  the 
same  French  or  Latin  words  as  ball;  but  bale  is  also 
an  old  name  for  evil,  calamity,  or  sorrow,  and  in  this 
meaning  comes  from  an  altogether  distinct  root.  The 


VI.] 


USE  OF  WORDS. 


25 


corn  which  we  eat  is  the  Latin  grannm , but  a corn 
or  horn  on  the  foot  is  the  Latin  cornu.  Bill 
means  either  William,  a document,  or  a hooked 
object,  for  instance,  the  bill  of  a bird.  In  each  case 
it  is  really  a different  word  similarly  spelt.  From 
such  confusions  of  "words  puns  and  humorous  mistakes 
may  arise,  but  hardly  any  important  errors. 

28.  In  most  cases  a word  changes  its  meaning  by 
degrees,  and  we  use  it  for  anything  which  is  close 
to,  or  connected  with,  the  first  meaning.  A bench 
means  a board  to  sit  on,  but  “ the  bench  ” is  a 
common  expression  for  the  row  of  magistrates  sitting 
on  the  bench.  A board  means  a broad  flat  piece  of 
wood,  but  being  often  used  to  support  the  dishes  at 
a meal,  people  speak  of  the  food  itself  as  the  board. 
Again,  because  a small  meeting  of  men  often  sit 
round  a table  for  convenience,  they  are  sometimes 
called  a board,  as  in  the  Board  of  Trade,  and  a small 
meeting-room  is  very  commonly  called  a board-room. 

29.  Any  word  which  has  two  or  more  meanings, 
and  is  used  in  such  a way  that  we  are  likely  to  con- 
fuse one  meaning  with  another,  is  said  to  be  am- 
biguous, or  to  have  the  quality  of  ambiguity.  By 
far  the  greater  number  of  words  are  ambiguous,  and 
it  is  not  easy  to  find  many  words  which  are  quite  free 
from  ambiguity.  Whether  we  are  writing,  or  reading, 
or  speaking,  or  merely  thinking,  we  should  always  be 
trying  to  avoid  confusion  in  the  use  of  words,  but  no 
one  can  hope  to  avoid  making  blunders  and  falling 
into  occasional  fallacies,  as  we  shall  learn  in  a later 
part  of  this  Primer. 

30.  In  many  important  cases  it  seems  almost  im- 
possible to  decide  exactly  what  a name  means. 
House,  for  instance,  has  a great  many  meanings.  No 
doubt,  it  first  meant  any  kind  of  roofed  building  in 
which  people  live  ; but,  as  the  shelters  made  for  cows 
much  resembled  houses,  they  were  called  cow-houses ; 

3 


26 


PRIMER  OF  LOGIC. 


[vi. 


and  we  speak  now  of  ice-houses,  tool-houses,  green- 
houses, hot-houses,  bathing-houses,  wash-houses,  and 
many  other  kinds  of  houses,  in  which  no  living  beings 
remain  long.  Counting-houses,  again,  being  the 
chambers  in  which  men  conduct  business,  we  often 
speak  of  the  house  instead  of  the  men,  just  as  we 
speak  of  the  bench  instead  of  the  magistrates. 
Thus  a commercial  house  means  a firm,  or  partner- 
ship, or  company  doing  business  together.  As  mem- 
bers of  Parliament  need  chambers  to  meet  and  debate 
in,  there  is  the  House  of  Lords,  and  the  House  of 
Commons,  and  it  is  usual  to  speak  of  “ The  House  ” 
meaning  the  collection  either  of  Lords  or  Commons 
who  happen  to  be  present.  Here  again  there  is 
ambiguity  ; for  the  House  of  Commons  may  mean 
either  the  members  who  happen  to  be  in  the  House 
at  any  particular  moment,  or  the  whole  body  of  652 
members  whose  right  and  duty  it  is  to  be  there  when 
the  Speaker  is  sitting. 

31.  Even  beyond  all  these  varieties  of  meaning, 
there  is  further  uncertainty  as  to  what  house  means 
when  it  is  merely  a dwelling-house.  Houses  are  of 
various  sizes,  and  if  a family  live  in  a building  having 
only  one  single  chamber,  it  would  be  a house. 
Legally  speaking,  the  head  of  the  family  would  be 
a householder.  If  several  poor  families  divide  a large 
house  between  them,  each  taking  one  or  two  rooms, 
we  still  speak  of  the  whole  building  as  one  house. 
Nevertheless,  it  is  for  practical  purposes  made  into 
several  houses.  If  a single  room  standing  alone 
makes  a house,  as  in  the  case  of  many  cottages,  why 
should  not  single  rooms  inhabited  by  different  families 
under  the  same  roof  make  different  houses  ? Whether 
there  is  or  is  not  an  outer  front  door  is  not  a matter 
of  real  importance.  If  in  this  way  we  follow  out  our 
use  of  the  word  house,  we  shall  find  that  we  cannot 
give  a satisfactory  account  of  it. 


VII.] 


CLASSIFICA  T10JV. 


27 


VII.— HOW  AND  WHY  WE  CLASSIFY  THINGS. 

32.  The  larger  number  of  terms,  as  we  have  learnt 
in  Art.  15,  are  the  names,  not  of  single  objects,  but 
of  many  objects,  or  rather  of  any  one  of  many 
objects.  “ Man  ” is  the  name  of  any  one  of  many 
hundreds  of  millions  of  men,  living  or  dead.  We 
have  hitherto  called  such  names,  general  names 
or  terms ; but  we  may  now  say  that  they  are  the 
names  of  classes  of  things,  provided  that  we 
take  great  care  to  ascertain  exactly  what  we  mean  by 
a class. 

We  class  things  together  whenever  we 
observe  that  they  are  like  each  other  in  any 
respect,  and  therefore  think  of  them  to- 
gether. Milk,  chalk,  snow,  meerschaum,  paper,  mist, 
spray,  foam  of  the  sea,  pearls,  and  white  lead,  are 
very  different  things  in  most  points,  but  they  all  agree 
in  being  white.  Together  with  many  other  substances 
and  things,  they  are  put  together  in  thought  into  the 
class  of  white  things.  In  this  case  the  resem- 
blance is  only  in  regard  to  colour ; but  in  other  cases 
there  may  be  many  points  of  resemblance. 

The  class  of  things  called  “pens,”  for  instance, 
includes  things  made  of  quills,  reeds,  steel,  gold, 
silver,  glass,  and  some  other  substances ; the  forms  of 
pens  also  differ ; nevertheless,  they  are  all  like  each 
other  in  being  made  to  hold  fluid  ink,  and  to  spread 
it  over  paper. 

33.  There  is  nothing  more  useful  than  to  be  able 
to  classify  things  correctly  and  easily,  and  to  form 
exact  general  notions  about  them.  So  far  as  things 
are  exactly  alike,  whatever  is  true  of  one 
thing  will  be  true  of  the  others,  which  so 
resemble  each  other.  When  we  classify 
things  correctly,  we  ascertain  the  exact 


PRIMER  OF  LOGIC. 


[VII. 


2S 


nature  and  degree  of  their  resemblances,  and 
record  the  information  we  have  gained  in 
the  briefest  and  most  convenient  form.  Our 

knowledge  is  increased  to  the  utmost,  and,  instead  of 
being  obliged  to  remember  an  immense  number  of 
disconnected  facts,  we  have  only  to  comprehend  a 
comparatively  small  number  of  general  truths.  To 
take  a very  simple  case,  we  class  together  white  things 
because  they  all  act  in  the  same  way  with  respect  to 
light.  Linen,  snow,  chalk,  cloud,  and  porcelain,  are 
exceedingly  different  in  other  respects,  so  that  it  is 
only  with  regard  to  light  that  we  expect  the  same  fact 
to  be  true  of  all  of  them.  Those  who  walk  over  a 
large  extent  of  snow  when  the  sun  is  shining,  find 
their  eyes  painfully  affected  by  the  glare  of  the  light 
reflected  from  the  snow.  They  might  expect  therefore 
that  the  same  effect  would  follow  from  walking  over 
a large  extent  of  ground  covered  with  white  chalk, 
white  dust,  or  white  linen  laid  out  to  bleach  in  the 
sun.  Again,  when  we  want  to  reflect  light  we  shall 
know  that  we  ought  to  use  white  substances;  in  a 
dark  room  we  should  have  a white  ceiling,  and  white 
paper  or  paint  on  the  walls.  If  there  be  walls  in 
front  of  a window,  they  should  be  built  of  white-faced 
bricks,  or  covered  with  white-wash,  if  we  want  ad- 
ditional light  in  the  room,  and  white  bricks  are  often 
used  for  this  purpose  at  the  present  day.  Sometimes, 
too,  whiteness  will  assist  us  in  avoiding  the  effects  of 
the  excessive  intensity  of  the  sun’s  rays  ; people  in 
tropical  countries  wear  white  clothes  and  hats  with 
this  object,  and  roofs  are  sometimes  white-washed  in 
order  that  they  may  absorb  less  of  the  sun’s  heat. 
All  these  results  follow  from  the  one  general  truth  or 
law  that  white  things  reflect  rays  of  light. 

34.  The  studies  of  botanists  and  other  naturalists 
are  chiefly  directed  to  classifying  plants  and  animals 
in  the  most  perfect  manner,  because  it  is  only  by 


VII.] 


CLASSIFICA  TION. 


29 


classification  that  we  can  possibly  remember  or  un- 
derstand the  characters  of  the  immense  numbers  of 
living  things.  All  kinds  of  grasses,  including  wheat, 
barley,  oats,  and  other  kinds  of  corn,  belong  to  one 
very  well-marked  class.  Any  one  having  a moderate 
knowledge  of  botany  can  tell  with  ease  whether  a 
given  plant  is  a kind  of  grass  or  not.  Now  the  food 
both  of  men  and  brutes  is  chiefly  derived  from  some 
sort  of  grass,  and  it  is  believed  with  much  reason  that 
no  plant  belonging  to  the  class  is  poisonous.  Hence 
a traveller  in  want  of  food  in  an  uninhabited  country 
might  always  eat  the  seeds  of  any  kind  of  grass 
without  fear.  On  the  other  hand,  plants  belonging  to 
the  order  Lobeliace/z  should  never  be  eaten,  as  most  if 
not  all  of  them  are  dangerously  poisonous.  The  same 
may  be  said  of  the  flowers  and  berries  of  plants 
belonging  to  the  order  of  Sotanacece,  among  which 
is  the  Deadly  Night-shade.  A good  botanist  would 
know,  almost  at  a glance,  that  these  and  many  other 
classes  of  plants  were  to  be  avoided,  or  very  carefully 
used. 

35.  It  is  somewhat  the  same  with  classes  of  sub- 
stances or  living  beings.  The  properties  of  the  class 
“man”  are  exceedingly  numerous.  The  surgeon  who 
has  well  studied  anatomy  knows  almost  exactly  the 
form  and  place  of  every  bone,  tendon,  muscle,  nerve, 
gland,  or  other  organ.  There  are  various  circum- 
stances in  which  one  man  may  differ  from  another ; 
these  are  in  logic  called  accidents.  An  organ  or 
muscle  may  be  smaller  or  larger  in  one  man  than 
another;  but  it  will  be  present  in  all,  so  that  the 
possession  of  the  organ  is  a property  of  the  man. 
Chemical  substances,  again,  have  innumerable  well- 
marked  properties.  If  a chemist  meets  with  a trans- 
parent colourless  crystal,  and  decides  by  certain 
tests  that  it  is  composed  of  carbonate  of  lime,  he 
knows  at  once  how  it  will  behave,  if  treated  with 


30  PRIMER  OF  LOGIC.  [vix. 

various  acids,  or  if  burnt  in  the  fire  ; for  he  knows 
the  properties  which  belong  to  all  portions  of  car- 
bonate of  lime. 

36.  In  classifying  things,  however,  we  must  take 
great  care  not  to  be  misled  by  outward  resemblances. 
Things  may  seem  to  be  very  like  each  other  which 
are  not  so.  Whales,  porpoises,  seals,  and  several 
other  animals  live  in  the  sea  exactly  like  fish  ; they 
have  a similar  shape,  and  are  usually  classed  among 
fish.  People  are  said  to  go  whale-fishing.  Yet  these 
animals  are  not  really  fish  at  all,  but  are  much  more 
like  dogs  and  horses  and  other  quadrupeds  than  they 
are  like  fish.  They  cannot  live  entirely  under  water 
and  breathe  the  air  contained  in  the  water  like  fish, 
but  they  have  to  come  up  to  the  surface  at  intervals 
to  take  breath.  Similarly,  we  must  not  class  bats 
with  birds  because  they  fly  about  ; although  they  have 
what  would  be  called  wings,  these  wings  are  not  like 
those  of  birds,  and  in  truth  bats  are  much  more  like 
rats  and  mice  than  they  are  like  birds.  Botanists 
used  at  one  time  to  classify  -plants  according  to  their 
size,  as  trees,  shrubs,  or  herbs,  but  we  now  know  that 
a great  tree  is  often  more  really  similar  in  its  character 
to  a tiny  herb  than  it  is  to  other  great  trees.  A daisy 
has  little  resemblance  to  a great  Scotch  thistle ; yet 
the  botanist  regards  them  as  very  similar.  The  lofty 
growing  bamboo  is  a kind  of  grass,  and  the  sugar- 
cane also  belongs  to  the  same  class  with  wheat  and 
oats. 

37.  In  classifying  a collection  of  objects,  we  do 
not  merely  put  together  into  groups  those  which  re- 
semble each  other,  but  we  also  often  divide  each 
larger  class  into  smaller  ones,  in  which  the  resemblance 
is  more  complete.  Thus,  the  class  of  white  substances 
may  be  divided  into  those  which  are  solid  and  those 
which  are  fluid,  so  that  we  get  the  two  minor  classes 
of  solid  white,  and  fluid  white  substances.  It  is 


VII.] 


CLASSIFICA  TION. 


3i 


desirable  to  have  names  by  which  to  show  that  one 
class  is  contained  in  another,  and  accordingly  we  call 
the  class  which  is  divided  into  two  or  more  smaller 
ones,  the  genus,  and  the  smaller  ones  into  which  it 
is  divided,  the  species.  Solid  white  substance  is  a 
species  of  the  genus  white  substance.  If  house  be 
taken  as  a genus,  then  dwelling-house  would  be  a 
species.  But,  when  we  like,  we  can  again  turn  the 
species  into  a genus,  by  dividing  it  up  a second  time ; 
thus,  brick  dwelling-house  would  be  a species  of  the 
genus  dwelling-house.  This  we  might  do  again  and 
again,  getting,  for  instance,  the  still  smaller  species, 
new  brick  dwelling-house,  large  new  brick  dwelling- 
house,  Elizabethan  large  new  brick  dwelling-house, 
and  so  on,  almost  without  limit. 

38.  It  is  often  a difficult  question  to  decide  how,  in 
any  particular  case,  we  can  best  divide  up  a large 
class  into  smaller  ones.  The  common  way  is  to  make 
as  many  species  all  at  one  step,  as  there  are  kinds  of 
things  belonging  to  the  class,  which  we  can  think  of 
at  the  time.  Thus,  we  might  divide  boats  into  sailing- 
boats,  steam-boats  and  row-boats.  Beasts  of  burden 
might  be  divided  into  horses,  mules,  donkeys,  camels, 
and  elephants.  Books  might  be  divided  into  those 
which  treat  of  History,  Geography,  Biography,  General 
Literature,  _ the  Physical  and  Moral  Sciences,  the 
Arts,  Political  Economy,  Theology,  Poetry,  Fiction, 
Periodical  Publications,  & c.  But,  in  making  such 

classifications,  we  are  almost  sure  to  fall  into  logical 
blunders. 

39-  In  the  first  place  the  species  or  small  classes 
are  likely  to  overlap  each  other,  unless  we  make  the 
divisions  with  much  care.  If  we  divide  the  people  of 
England  into  men,  women,  children,  paupers,  vagrants, 
blind,  deaf  and  dumb,  and  foreigners,  we  commit 
several  very  evident  blunders,  because  paupers,  blind, 
deaf  and  dumb,  as  well  as  foreigners,  must  be  either 


32 


PRIMER  OF  LOGIC. 


[vii. 


men,  women,  or  children,  so  that  if  they  were 
counted  once  in  that  respect  they  ought  not  to  be 
counted  again  as  paupers,  blind  persons,  &c.  Vagrants 
are  a kind  of  paupers,  and  often  difficult  to  distinguish 
from  them.  Moreover,  vagrants  and  foreigners  may 
happen  to  be  blind,  or  deaf  and  dumb.  In  dividing 
books,  again,  it  will  be  found  impossible  to  make  any 
classification  in  which  a book  shall  always  belong  to 
one  species  and  only  to  one.  The  species  will  be 
sure  to  overlap.  There  may  be  books  on  the  history 
of  science  which  might  be  equally  well  placed  in  the 
class  of  histories,  or  in  that  of  books  on  physical 
science.  There  may  be  books  which  are  half  bio- 
graphy, half  history.  Miss  Martineau’s  “Tales  on 
Political  Economy,”  might  be  placed  both  in  the  class 
of  fiction  and  in  that  of  political  economy.  Nobody 
can  be  sure  in  which  class  any  particular  book  will  be 
found,  and  accordingly  such  classifications  are  not 
only  logically  bad  ones,  but  they  are  of  little  use. 
Yet  we  find  them  employed  in  the  catalogues  of  many 
libraries. 

40.  A second  difficulty  is,  that,  in  planning  such 
classifications,  we  can  seldom  be  sure  of  making 
enough  species  to  include  all  the  things  belonging  to 
the  genus.  There  may  be  beasts  of  burden  which 
are  neither  horses,  mules,  donkeys,  camels,  nor  ele- 
phants ; for  instance,  the  llamas  used  in  South 
America,  yaks  in  Thibet,  and  oxen  in  many  parts  of 
the  world.  Boats  need  not  always  be  comprised 
under  sailing-boats,  steam-boats,  and  row-boats  ; thus, 
there  are  boats  with  paddle-wheels  worked  by  a 
handle  or  crank  inside  the  boat ; there  are  also  canal- 
boats  towed  by  horses  or  men,  ferry-boats  moved  by 
the  force  of  a river,  barges  which  go  up  and  down 
with  the  tide  in  a river. 

41.  All  these  difficulties  are  avoided  in  the  per- 
fect logical  method  of  dividing  each  genus 


VII.] 


CLASSIFICA  TION. 


33 


into  two  species  and  not  more  than  two,  so 
that  one  species  possesses  a particular  quality, 
and  the  other  does  not.  Thus,  if  I divide  dwell- 
ing-houses into  those  which  are  made  of  brick  and 
those  which  are  not  made  of  brick,  I am  perfectly  safe, 
and  nobody  can  find  any  fault  with  me.  Even  if  I do 
not  know  what  dwelling-houses  are  exactly,  yet  I may 
be  quite  sure  that  anything  which  is  a dwelling-house 
will  belong  either  to  the  species  made  of  brick,  or,  if 
not,  to  the  other  species  which  are  not  made  of  brick. 
But  this  would  not  be  the  case  if  I divide  the  genus 
at  one  step  into  many  species.  Suppose,  for  instance, 
that  I divide  dwelling-house  as  below : — 
Dwelling-House. 


Brick.  Stone.  Earth.  Iron.  Wood. 

The  evident  objection  will  at  once  be  made,  that 
houses  may  be  built  of  other  materials  than  those 
here  specified.  In  Australia  houses  are  sometimes 
made  of  the  bark  of  gum  trees ; the  Esquimaux  live 
in  snow  houses ; tents  may  perhaps  be  considered  as 
canvas  houses,  and  it  is  easy  to  conceive  of  houses 
made  of  terra-cotta,  paper,  straw,  &c.  All  logical  diffi- 
culties will  however  be  avoided  if  I never  make  more 
than  two  species  at  each  step,  in  the  following  way: — 
Dwelling-House. 

I ' 1 

Brick.  Not-brick. 


Stone.  Kot-stone. 


Wooden.  Not-wooden. 


Iron. 


Not-iron. 


34 


PRIMER  OF  LOGIC. 


[VII. 


It  is  quite  certain  that  I must  in  this  division  have 
left  a place  for  every  possible  kind  of  house  ; for  if  a 
house  is  not  made  of  brick,  nor  stone,  nor  wood,  nor 
iron,  it  yet  comes  under  the  species  at  the  right  hand, 
which  is  not-iron,  not-wooden,  not-stone,  and  not- 
brick. 

42.  If,  again,  we  divide  substances  into  the  two 
species,  solid  and  not  solid,  every  substance  must  fall 
into  one  or  the  other,  and  nothing  can  fall  into  both. 
No  doubt  there  are  degrees  of  solidity,  and  we  might 
meet  with  substances  such  as  tar,  treacle,  putty,  &c., 
which  might  be  said  to  be  in  a half  solid  state.  But, 
if  they  are  only  half  solid  they  must  not  be  put  into 
the  class  of  solid  things,  and  therefore  they  must  go 
into  the  class  of  things  which  are  not  solid.  If 
requisite  we  may  make  a new  class  of  viscid  things, . 
or  semi-fluid  things,  and  we  may  go  on,  time  after 
time,  making  divisions  in  the  same  way.  We  should 
get  some  such  series  of  divisions  as  the  following : — 

Substance. 


Solid.  Not-solid. 


Viscid.  Not-viscid. 


Liquid.  Not-liquid. 


Gas.  Not -gas. 

We  must  understand,  in  reading  the  above,  that 
liquid  things  are  both  not  viscid  and  not  solid,  and 
that  gas  is  not  liquid,  not  viscid,  and  not  solid.  No 
possible  logical  fault  can  be  found  with  this ; for,  if 
we  really  know  what  we  mean  by  a solid,  viscid, 
liquid,  and  gas,  any  substance  whatever  must  fall 


VII.] 


CLASSIFICA  TION. 


35 


under  one  division  and  only  one.  If  we  can  find  any 
substance,  such  as  india-rubber  or  jelly,  which  does 
not  correspond  to  any  of  the  descriptions  of  solid, 
viscid,  liquid,  or  gas,  there  still  remains  a division 
provided  for  it,  namely,  that  of  not  solid,  not  viscid, 
not  liquid,  not  gas. 

This  manner  of  classifying  things  may  seem  to  be 
inconvenient,  but  it  is  in  reality  the  only  truly  logical 
way.  Other  methods  of  dividing  a genus  into  species 
are  only  correct  so  far  as  they  are  constructed  on  the 
same  principle,  though  this  may  not  be  apparent. 

43.  Let  us  inquire  exactly  what  we  do  when  we 
take  brick-dwelling-house  as  a species  of  the  genus 
dwelling-house.  There  are  certainly  not  so  many 
brick-dwelling-houses  as  there  are  dwelling-houses, 
because  we  exclude  from  the  species  all  stone,  wood, 
iron,  or  other  kinds  of  dwelling-houses.  Thus  we  find 
that  the  species  has  a narrower  extension 
than  the  genus  (Art.  22).  In  one  way  it  has  less 
meaning  than  the  genus,  because  there  are  fewer 
objects  called  brick-dwelling-houses,  than  those  which 
may  be  called  dwelling-houses.  But  in  another  point 
of  view  there  is  more  meaning  in  the  species  than 
in  the  genus,  because  we  know  more  about  the  things. 
We  know  that  anything  placed  in  the  class  brick- 
dwelling-house is  not  merely  a dwelling-house,  but 
that  it  is  made  of  bricks.  This  we  may  express  by 
saying  that  the  species  has  greater  intension 
than  the  genus,  meaning  by  intension  (Art.  22) 
the  number  of  qualities  which  belong  to  all  things  in 
the  class. 

44.  The  quality  by  which  a genus  is  divided  into 
two  or  more  species  is  called  the  difference.  In 
the  last  article,  brick,  or  “ made  of  brick,”  is  the 
circumstance  by  which  the  species  of  brick-dwelling- 
houses  is  distinguished  from  all  other  dwelling-houses. 
Thus  we  may  be  said  to  add  the  quality  “ made  of 


36  PRIMER  OF  LOGIC.  [vir. 

brick  ’’  to  the  qualities  of  a dwelling-house,  in  order 
to  get  the  qualities  of  the  species  we  want.  These 
qualities,  namely  those  common  to  all  of  the  genus, 
with  the  difference  added,  make  the  definition  of  the 
species.  By  a definition  we  mean  a precise 
statement  of  the  qualities  which  are  just 
sufficient  to  mark  out  a class,  and  to  tell  us 
exactly  what  things  belong  to  a class  and  what  do 
not.  Nothing  is  more  important  than  to  be  able  to 
define  clearly  the  classes  of  things  about  which  we 
are  debating,  but  this  is  often  a difficult  task.  In 
this  case  the  definition  of  brick-dwelling-house,  will 
consist  of  the  difference,  “brick,”  added  to  the  de- 
finition of  dwelling-house,  which  again  might  be  said 
to  consist  of  the  circumstance  that  the  house  is  used 
for  dwelling  in,  added  to  the  definition  of  a house. 

45.  We  must  not  suppose  for  a moment  that  all 
the  qualities  of  a thing  are  to  be  included  in  its 
definition.  A certain  quality  may  belong  to  some 
of  a class  and  not  to  others,  in  which  case  it  obviously 
cannot  be  part  of  the  definition.  Some  bricks  are 
red,  some  white,  and  some  blue ; the  quality  redness, 
then,  will  be  no  part  of  the  definition  of  brick-dwelling- 
house,  but  will  be  said  to  be  an  accident  of  the 
species.  Thus  by  an  accident  we  mean  any  quality 
or  circumstance  which  may  or  may  not  belong  to  a 
class,  accidentally  as  it  were.  There  are  other  qualities 
which  belong  to  the  whole  of  a class  and  yet  are 
not  regarded  as  part  of  the  definition.  Such  quali- 
ties are  called  properties  of  the  class.  We 
might  perhaps  say  that  it  is  a property  of  all  brick 
dwelling-houses  to  be  durable.  It  is  a property  of 
the  class  mushroom  to  be  good  to  eat ; it  is  a pro- 
perty of  all  the  large  class  of  grasses  to  be  not 
poisonous. 

46.  It  will  now  be  understood  how  important  it  is 
to  be  able  to  classify  and  define  things  accurately, 


VIII.] 


PROPOSITIONS. 


37 


because  when  once  we  can  do  this,  the  properties 
which  belong  to  the  things  will  also  be  readily  known. 
The  qualities  of  the  things  which  we  meet  with  around 
us  are  not  mixed  up  without  order,  but  some  of  them 
follow  from  or  are  attached  to  other  qualities.  This 
is  very  well  seen  in  the  case  of  geometrical  figures. 
We  define  the  species  triangle,  as  containing  “ three- 
sided  rectilinear  figures.”  The  genus  is  rectilinear 
figure,  or  figure  made  entirely  of  straight  lines,”  and 
the  difference  is  “ three-sided,”  by  which  triangles  are 
distinguished  from  figures  of  four,  five,  or  more  sides. 
But  triangles  besides  being  three-sided  rectilinear 
figures  have  many  other  properties  always  present. 
The  three  angles  of  a triangle,  when  added  together 
always  make  exactly  two  right  angles.  If  lines  be 
drawn  through  the  middle  of  each  side  of  a triangle 
perpendicularly  to  the  side,  they  will  all  meet  in  one 
point,  and  so  will  lines  drawn  through  the  angles,  and 
dividing  them  equally.  There  are  a great  many  other 
circumstances  true  of  all  triangles,  as  maybe  learnt 
in  any  book  on  geometry,  and  all  these  may  be 
rightly  called  properties  of  triangles.  A circle  may 
be  defined  as  a plane  figure,  every  point  in  the 
boundary  of  which  is  equally  distant  from  a single 
point,  but  the  properties  of  circles  are  exceedingly 
numerous,  and  are  not  fully  described  in  any  book. 


VIII.— PROPOSITIONS. 

47.  Having  now  sufficiently  learnt  the  nature  and 
use  of  logical  terms,  we  come  to  the  second  part  of 
logic,  which  describes  propositions.  As  we  learned  at 
the  beginning  (Art.  11),  an  ordinary  proposition  joins 
two  terms  together  by  means  of  a verb  called  a 
copula.  It  is  only  when  we  thus  assert  some  agree- 
ment or  connection  between  terms,  or  assert  one 
4 


PRIMER  OF  LOGIC. 


[vin. 


thing  of  another  that  we  can  be  said  to  be  right  or 
wrong.  If  I were  to  say  “ The  weather  ” without 
saying  anything  more,  no  one  could  know  what  I 
meant,  or  whether  I meant  anything  at  all.  Nobody 
could  answer  me,  or  say  that  I was  either  right  or 
wrong.  But,  if  I say  “ The  weather  is  hot  ” people 
can  judge  whether  there  is  an  agreement  between 
the  terms  corresponding  with  what  they  feel.  Let 
us  inquire  exactly  what  is  the  meaning  of  a proposi- 
tion. 

Take  as  an  example  “ Coins  are  metallic.”  Here 
we  have  one  concrete  general  term,  Coins,  joined  to 
another  concrete  general  term,  metallic,  which  may  be 
considered  to  mean  “ made  of  metal.”  The  proposition 
states  that  the  quality  of  being  made  of  metal  belongs 
to  all  coins.  The  things  about  which  we  are  chiefly 
thinking  are  coins,  and  the  term  coins  is  therefore 
said  to  form  the  subject  of  the  proposition.  In 
most  cases  we  may  know  the  subject  of  a proposition 
by  its  being  put  first.  The  copula  “are”  comes  next, 
and  joins  the  subject  to  words  indicating  the  quality 
which  belongs  to  it,  namely  “ metallic.”  This  is  called 
the  predicate  of  the  proposition,  which  is  merely 
a word  derived  from  the  Latin,  and  meaning  that 
which  is  stated  or  affirmed.  A proposition 
consists,  then,  of  subject,  copula,  and  predicate  in  the 
order  as  thus  stated. 

48.  W e may  explain  the  meaning  of  a proposition 
in  another  way,  which,  however,  comes  to  the  same 
thing  in  the  end.  There  are  great  numbers  of  coins 
in  the  world,  and  still  greater  numbers  of  things  made 
of  metal.  When  we  say  “ Coins  are  made  of  metal,” 
we  assert  that  all  coins  will  be  found  among  the 
things  made  of  metal.  If  we  could  imagine  all  the 
metallic  things  in  the  world  put  into  a heap  together, 
and  if  we  then  picked  the  coins  out  of  them,  we  should 
get  all  possible  coins,  because,  if  there  were  any  not 


VIII.] 


PROPOSITIONS. 


39 


in  the  supposed  heap,  they  would  not  be  made  of 
metal,  all  things  so  made  having  been  put  into  this 
heap.  We  come  to  this  result  then,  that  a proposition 
of  the  kind  described  asserts  that  the  subject  is 
the  name  of  a thing,  or  class  of  things,  con- 
tained among  the  more  numerous  things  of 
which  the  predicate  is  the  name. 

49.  I have  said  that  a proposition  consists  of  sub- 
ject, copula,  and  predicate  joined  together  in  the 
order  as  stated.  But  they  are  not  always  given  in  this 
way  in  writing  and  speaking.  Sometimes  the  propo- 
sition is  inverted  and  the  predicate  is  put  first,  as  in 
“ Blessed  are  the  peacemakers,”  “ Strong  is  truth.” 
In  such  cases  we  must  judge  as  well  as  we  can  which 
is  the  subject  and  which  the  predicate  by  the  charac- 
ter of  the  words  or  their  meanings.  Thus  the  words 
“blessed”  and  “strong”  being  both  adjectives  are 
evidently  predicates.  Very  commonly,  again,  the 
copula  is  not  distinctly  expressed  but  is  contained  in 
a verb.  “ The  sun  shines  ” seems  to  be  a proposition 
with  two  terms  and  no  copula,  but  it  really  means 
“The  sun  is  shining.”  In  Latin  a single  verb  may 
make  a complete  proposition,  as  in  “Amo,”  I love. 
When  Caesar  said  “ Veni,  Vidi,  Vici,”  I came,  I saw, 
I conquered,  he  expressed  three  complete  propositions 
in  three  words.  The  science  of  language,  however, 
shows  that  each  of  these  single  words  arose  from  the 
joining  together  of  the  subject,  copula,  and  predicate, 
in  the  same  way  that  we  shorten  “ I am  ” into  “ I’m,” 
or  “ do  not  ” into  “ don’t.” 

50.  There  are,  however,  various  kinds  of  proposi- 
tions, and  that  as  yet  considered  belongs  to  the 
affirmative  kind.  Negative  propositions,  on 
the  contrary,  assert  that  the  subject  is  not  con- 
tained among  the  predicate.  When  I say 
“ Coins  are  not  combustible  ” I think  at  the  same 
time  of  two  classes  of  things,  “ Coins  ” and  “ com- 


40 


PRIMER  OF  LOGIC. 


[vm. 


bustible  things;”  but  I come  to  the  conclusion  that 
the  coins  would  not  be  found  among  combustible  sub- 
stances, such  as  wood,  coal,  oil,  gas.  If  we  had  a 
museum  which  contained  nothing  but  combustible 
things,  there  would  not  be  a single  coin  shown  in  it. 
Similarly,  in  a museum  of  coins  we  shall  not  find  any 
combustible  thing  shown  as  a coin.  Thus  the  nega- 
tive proposition  in  question  asserts  that  the  subject 
and  predicate  are  altogether  separate,  and  that  no 
object  belonging  to  the  one  class  is  found  likewise  in 
the  other.  We  may  know  a negative  proposition  by 
its  containing  the  little  word  “ not,”  or  it  may  be 
“no;”  but  sometimes  such  words  as  “never”  or 
“ nowhere  ” are  used  to  make  negative  propositions. 

51.  So  far  it  has  seemed  as  if  there  were  only  two 
kinds  of  propositions,  affirmative  and  negative.  But, 
before  we  go  on,  I ought  to  say  that  propositions  may 
be  divided  in  a quite  different  way.  Hypothetical 
propositions  do  not  positively  assert  the  predicate  of 
the  subject,  except  under  certain  circumstances.  Thus, 
“ if  water  be  boiling,  it  will  scald  ” is  a hypothetical 
proposition  asserting,  not  that  all  water  will  be  found 
among  scalding  things,  but  that,  when  it  is  boiling,  it 
will  scald.  “If  gunpowder  be  damp,  it  will  not  ex- 
plode ; ” this  is  a negative  hypothetical  proposition  ; 
for  it  asserts  that  gunpowder,  when  it  happens  to  be 
damp,  will  not  be  found  among  exploding  things. 
Hypothetical  propositions  may  generally  be  recognised 
by  containing  the  little  word  “if;”  but  it  is  doubtful 
whether  they  really  differ  much  from  the  ordinary 
yiropositions  already  considered.  We  may  easily  say 
“boiling  water  will  scald,”  and  “damp  gunpowder  will 
not  explode,”  thus  avoiding  the  use  of  the  word  “if.” 

52.  Propositions  belonging  to  a third  class  are 
called  disjunctive,  and  contain  the  little  conjunction 
“ or,”  sometimes  together  with  “ either.”  As  exam- 
ples we  may  say:  “Lightning  is  sheet  or  forked;” 


VIII.] 


PROPOSITIONS. 


4l 


“ Arches  are  either  round  or  pointed  ; ” “ Angles  are 
either  obtuse,  or  right  angled,  or  acute.”  These  pro- 
positions, as  we  see,  contain  more  than  one  predicate, 
and  do  not  say  to  which  the  subject  belongs.  Arches 
are  not  always  round,  and  if  not  round  are  pointed, 
and  if  not  pointed  they  are  round.  There  is  a choice 
of  predicates.  Disjunctive  propositions  are  very  im- 
portant, but  more  difficult  to  understand  than  other 
kinds  of  propositions,  and  it  will  be  convenient  to 
leave  their  further  consideration  until  after  we  have 
learnt  the  nature  of  syllogistic  reasoning. 

53.  We  have  already  learnt  that  propositions  may 
be  affirmative  or  negative.  They  differ  also  as  regards 
what  is  called  the  quantity  of  the  proposition, 
which  depends  upon  the  quantity  of  the  subject  of 
which  the  predicate  is  held  to  be  true.  When  I say 
“All  clouds  in  the  sky  are  composed  of  particles  of 
water  ” I mean  to  assert  that  the  whole  quantity  of 
clouds  appearing  high  up  in  the  atmosphere  are  to  be 
found  among  things  composed  of  minute  particles  of 
water.  There  are  other  things  also  formed  of  such 
particles,  namely  mists,  fogs,  spray,  steam,  &c.  I may 
say  then  that  the  predicate  in  this  proposition  be- 
longs universally  to  all  clouds  in  the  sky,  and  the 
statement  is  accordingly  called  a universal  pro- 
position. 

54.  If  I say  again,  “ Some  persons  are  deaf-mutes,” 
the  quantity  of  the  subject  persons  is  said  to  be  parti- 
cular, because,  as  shown  by  the  little  adjective  “some,” 
I do  not  intend  to  assert  that  more  than  a portion  of 
the  subject  “persons”  are  known  to  be  in  the  class 
of  deaf-mutes.  Every  proposition  in  which  the  pre- 
dicate is  stated  to  belong  to  a part  of  the  subject  is 
called  a particular  proposition.  As  other  in- 
stances I may  mention  such  as  the  following  : “ a few 
Englishmen  can  speak  Chinese  ; ” “ many  Englishmen 
emigrate ; ” “ certain  books  are  intended  only  for 


42 


PRIMER  OF  LOGIC. 


[viii. 


reference  ; ” “ most  storms  are  preceded  by  a fall  of 
the  barometer.”  Particular  propositions  may  be  either 
negative  or  affirmative  ; thus,  “ some  well-water  is  not 
fit  to  drink”  is  a particular  negative  proposition. 
Universal  propositions  also  may  be  either  negative  or 
affirmative,  so  that  as  twice  two  make  four,  there  come 
to  be  four  principal  kinds  of  propositions,  namely, 
universal  affirmative  propositions,  universal  negative 
propositions,  particular  affirmative  propositions,  and 
particular  negative  propositions.  We  must  go  on  to 
inquire  more  exactly  into  the  nature  and  meaning  of 
each  of  these  four  kinds  of  propositions. 

55.  When  we  intend  to  make  a statement  about  all 
the  things  which  can  be  included  under  a term,  we 
are  said  to  take  the  term  universally,  or  as  logicians 
often  say,  the  term  is  distributed.  In  the  propo- 
sition “all  coins  are  made  of  metal,”  the  term  “coins,” 
as  already  explained,  is  taken  universally,  or  is  distri- 
buted, because  the  little  adjective  “all  ” indicates  that 
the  statement  applies  to  any  and  every  coin.  But 
the  predicate  is  only  taken  particularly  and 
is  not  distributed  ; it  would  be  absurd  to  suppose 
that  we  intended  to  state  that  all  things  made  of 
metal  are  coins.  We  can  only  have  meant  that  all 
coins  are  among  things  made  of  metal,  or  are  a part 
of  them,  and  there  exists,  of  course,  an  almost  number- 
less variety  of  other  things  made  of  metal.  We  must 
carefully  remember  then  that  a universal  affir- 
mative proposition  like  the  one  we  have  been 
examining,  distributes  its  subject,  but  does  not 
distribute  its  predicate. 

56.  We  may  show  very  clearly  the  exact  meaning 
of  a proposition  by  imagining  that  the  things  we  are 
speaking  of  are  included  in  circles,  like  sheep  in 
sheep-pens.  Imagine  that  all  things  made  of  metal 
and  only  such  are  put  in  the  larger  circle  in  Fig.  1, 
and  all  coins  in  the  smaller  circle.  As  the  smaller 


VIII.] 


PROPOSITIONS. 


43 


circle  lies  within  the  larger  one,  it  follows  that  all  coins 
are  included  among  things  made  of  metal,  there  being 


nothing  but  such  inside  the  larger  circle.  We  shall 
often  find  it  convenient  to  use  circles  to  show  how  one 
class  or  term  is  included  wholly  or  partly  in  another, 
or  excluded  from  it,  as  the  case  may  be. 

57.  As  a universal  negative  proposition,  let  us  take 
“No  sea-weed  is  a flowering  plant,”  and  inquire  care- 
fully what  this  means.  It  evidently  speaks  of  all 
sea-weeds,  so  that  the  subject  is  distributed ; but  does 
it  take  the  predicate,  flowering  plant,  in  a universal 
sense  ? Our  answer  should  depend  upon  whether  or 
not  we  must  examine  all  flowering  plants  before  we 
decide  that  no  sea-weed  is  a flowering  plant.  But,  if 
we  omitted  to  consider  a single  flowering  plant,  and 
this  proved  to  be  a sea-weed,  our  proposition  would 
be  untrue.  The  proposition  asserts,  then,  that  no 
sea-weed  is  the  same  as  any  flowering  plant,  so  that 
there  is  complete  separation  between  the  two  classes, 
and  no  object  can  be  placed  in  both  classes. 

58.  We  may  show  this  in  Fig.  2,  the  circle  sup- 
posed to  contain  all  sea-weeds  lying  quite  outside 
of  the  circle  containing  all  flowering  plants. 

If  any  part  of  one  circle  were  to  lie  over  part  of 
the  other,  some  objects  would  be  in  both  classes, 


44 


PRIMER  OF  LOGIC. 


[viii. 


whereas  the  proposition  asserts  that  no  sea-weed  is 
in  any  part  of  the  class  dowering  plant.  We  arrive, 


then,  at  this  important  truth,  which  should  be  carefully 
borne  in  mind,  that  the  universal  negative  pro- 
position distributes,  or  takes  universally, 
both  its  subject  and  its  predicate. 

59.  We  shall  have  no  difficulty  in  seeing  that  a 
particular  affirmative  proposition  distributes 
neither  its  subject  nor  its  predicate.  Take 
as  an  example,  “some  violets  are  odorous.”  The 
subject  “violets”  is,  of  course,  undistributed,  because 
the  proposition  is  particular.  The  predicate,  moreover, 
is  undistributed ; for  it  cannot  be  supposed  that  we 
intended  to  say  that  some  violets  are  the  only  odorous 
things.  There  are  a multitude  of  other  flowers,  and 
many  substances  which  are  odorous  in  addition  to 
violets,  so  that  the  proposition  must  be  taken  as 
“ some  violets  are  some  odorous  things,”  or  a part 
of  odorous  things.  The  predicate,  then,  as  well  as 
the  subject,  is  taken  particularly,  or  is  undistributed. 

As  other  examples  of  the  same  kind  of  proposition 
I might  mention  the  following  : — many  foolish  novels 
are  published ; most  tunes  in  a minor  key  are  melan- 
choly ; a few  specimens  of  Saxon  architecture  still 
exist ; threepenny  pieces  are  sometimes  mistaken  for 
fourpenny  pieces. 


VI II.  ] 


PROPOSITIONS. 


45 


60.  Coming,  lastly,  to  a particular  negative  pro- 
position, say  “ some  violets  are  not  odorous,”  we 
know  that  the  subject  is  undistributed,  but  we 
may  easily  discover  that  the  predicate  is 
distributed.  Unless  the  some  violets,  of  which  we 
are  speaking,  were  quite  shut  out  of  the  class  of 
odorous  things,  it  would  be  untrue  that  they  were 
inodorous.  Hence  we  really  mean  that  “ some  violets 
are  not  any  odorous  things,”  so  that  the  predicate 
“odorous  things”  is  taken  universally. 

6 1.  When  we  try  to  show  the  meaning  of  particular 
propositions  by  using  circles,  it  is  difficult  to  avoid 
mistakes  ; but  we  often  make  mistakes  of  the  same 
kind  in  thinking  and  talking,  and  it  is  well  to  be 
aware  of  the  fact.  When  we  say  “ some  violets  are 
odorous,”  we  should  generally  be  supposed  to  mean 
that  “ some  violets  ” are  so,  and  others  are  not ; but 
in  this  case  one  affirmative  proposition  really  means 
the  same  as  an  affirmative  one  and  a negative  one 
put  together,  namely  : — - 

Some  violets  are  odorous ; 

Some  violets  are  not  odorous. 

But  it  is  not  logical  to  say  one  thing  and  mean 
another.  When  we  say  “ some  violets  are  odorous,” 
we  ought  to  be  understood  as  meaning  simply  that 
“ some  are,”  leaving  it  quite  uncertain  whether  other 
violets  are  or  are  not.  In  many  cases  we  really 
should  not  know.  I may  safely  say,  for  instance,  that 
“ some  dogs  are  descended  from  wolves,”  it  being 
nearly  certain  that  some  dogs  are  so ; but  it  may 
be  afterwards  ascertained  that  all  dogs  are  so  des- 
cended, or,  on  the  contrary,  that  some  are  not  so. 
I may  say  again  that  “ some  metals  are  combustible,” 
without  meaning  to  say  that  some  are  not.  I may 
correctly  .say  that  “ some  men  or  most  men  laugh,” 
without  staying  to  inquire  carefully  whether  all  men 


46 


PRIMER  OF  LOGIC. 


[VIII. 


do  as  a fact  laugh.  Not  being  sure  that  some  men 
do  not  laugh,  I must  not  be  supposed  to  assert  this, 
in  saying  that  some  do.  In  the  absence  then  of  any 
knowledge  to  the  contrary,  the  word  some  must 
be  taken  to  mean  “ some  and  it  may  be  all.” 
I may  safely  say  “ some,  and  it  may  be  all,  dogs 
are  descended  from  wolves,”  though  it  may  afterwards 
be  shown  to  be  untrue  that  all  dogs  are  so  descended. 

6 2.  Returning  to  the  use  of  circles  to  show  the 
meaning  of  the  propositions  in  question  we  meet  a 
similar  difficulty.  If  I draw  two  circles  crossing  each 
other  as  in  Fig.  3,  and  fill  one  circle  with  violets  and 


the  other  with  odorous  things,  the  figure  evidently 
means  that  part  of  the  class  violets  is  in  the  class 


odorous  things ; but  then  another  part  of  the  same 
class  violets  is  outside  the  odorous  things,  so  that 


IX.] 


PROPOSITIONS. 


47 


both  the  particular  affirmative  and  the  particular 
negative  are  shown  at  the  same  time.  To  avoid  the 
difficulty  we  might  perhaps  use  a circle  with  a part 
of  its  circumference  broken.  Thus,  Fig.  4 would 
show  that  there  certainly  existed  some  violets  inside 
the  circle  of  odorous  things,  but  the  broken  line 
might  be  understood  to  mean  that  it  was  doubtful 
whether  or  not  any  violets  were  really  outside  the 
odorous  things.  Such  a figure  then  indicates  the 
meaning  of  the  particular  affirmative  proposition.  If 
the  broken  part  of  one  circle  lies  inside  the  other 
circle,  as  in  Fig.  5,  the  meaning  will  evidently  be  that 


some  violets  are  known  to  be  outside  the  odorous 
things,  but  that  it  is  doubtful  whether  some  violets 
are  inside  or  not.  This  is  the  true  meaning  of  the 
particular  negative  proposition. 

IX.— HOW  TO  CHANGE  PROPOSITIONS. 

63.  Having  now  carefully  learned  the  nature  of 
each  of  the  four  chief  kinds  of  propositions,  we  must 
consider  various  ways  in  which  we  can  draw  or  infer 
one  proposition  from  another.  We  can  often  put  the 
same  truth  into  different  words,  just  as  we  can  mould 
the  same  clay  into  different  forms,  though  it  always 
remains  the  same  clay.  We  can  do  likewise  with 


43 


PRIMER  OF  LOGIC. 


[ix. 


propositions ; it  comes  to  the  same  thing,  for  instance, 
whether  I say  “ all  coins  are  metallic,’'  or  “ no  coins 
are  not  metallic  ; ” or  again  “ there  are  no  coins  which 
are  not  metallic.” 


64.  If,  using  circles  again  (see  Fig.  6),  we  sup- 
pose all  metallic  things  to  fill  up  the  larger  circle,  it 
follows  that  everything  which  is  not  metallic  is  outside 
the  circle ; and,  as  all  coins  are  supposed  to  be 
within  the  smaller  circle,  included  in  the  greater  one, 
it  follows  that  none  of  the  coins  can  be  outside  the 
greater  circle,  or  among  non-metallic  things.  It  is 
evidently  the  same  in  the  end  to  say  that  all  coins 
are  within  the  circle  of  metallic  things,  and  that  none 
of  them  are  outside.  In  this  way  we  can  always 
change  a universal  affirmative  proposition  into  a 
universal  negative  one  of  the  same  meaning,  and  we 
can  make  the  change  backwards  again.  Thus,  to  say 
“ there  are  no  things  which  may  not  be  useful,”  is 
oniy  a longer  way  of  saying,  “ all  things  may  be 
useful.”  It  is  very  desirable  that  the  reader  should 
practise  himself  in  quickly  and  correctly  making  this 
and  several  other  changes  of  propositions  which  I 
shall  describe. 

65.  We  can  always  change  a proposition  by  turning 
it  about,  so  as  to  make  the  old  subject  into  a new 


IX.] 


PROPOSITIONS. 


49 


predicate,  and  the  old  predicate  into  a new  subject. 
We  are  then  said  to  convert  the  proposition, 
and  the  new  proposition  is  called  the  converse  of 
the  old  one.  But  it  does  not  follow  that  the  new  one 
will  always  be  true  if  the  old  one  was  true.  Some- 
times this  is  the  case,  and  sometimes  it  is  not.  If 
I say,  “ some  churches  are  wooden  buildings,”  I may 
turn  it  about  and  get,  “ some  wooden  buildings  are 
churches ; ” the  meaning  is  exactly  the  same  as  before. 
This  kind  of  change  is  called  simple  conversion, 
because  we  need  do  nothing  but  simply  change  the 
subjects  and  predicates  in  order  to  infer  a new  pro- 
position. We  see  that  the  particular  affirmative 
proposition  can  be  simply  converted.  Such 
is  the  case  also  with  the  universal  negative  proposition. 
“No  large  flowers  are  green  things”  maybe  converted 
simply  into  “no  green  things  are  large  flowers,”  by 
merely  writing,  “ green  things  ” in  place  of  “ large 
flowers,”  and  large  flowers  instead  of  “ green  things.” 


Using  circles  (see  Fig.  7),  since  the  green  things  are 
quite  separated  from  the  large  flowers,  it  evidently 
follows  that  the  large  flowers  are  quite  separated  from 
the  green  things. 

66.  It  is  a more  troublesome  matter,  however,  to 
convert  a universal  affirmative  proposition.  The 
statement  that  “all  jellyfish  are  animals,”  is  true; 

5 


5° 


PRIMER  OF  LOGIC. 


[IX. 


but,  if  we  simply  convert  it,  getting  “all  animals  are 
jelly  fish,”  the  result  is  absurd.  This  is  because,  as 
we  learned  before  (Art.  55),  the  predicate  of  a uni- 
versal affirmative  proposition  is  really  particular.  We 
do  not  mean  to  say  that  jelly  fish  are  “ all  ” the 
animals  which  exist,  but  only  “ some  ” of  the  animals. 
The  proposition  ought  really  to  be,  “all  jelly  fish  are 
some  animals,”  and  if  we  converted  this  simply,  we 
should  get,  “ some  animals  are  all  jelly  fish.”  But  we 
almost  always  leave  out  the  little  adjectives  some  and 
all  when  they  would  occur  in  the  predicate,  so  that 
the  proposition,  when  converted,  becomes  “ some 
animals  are  jelly  fish.”  This  kind  of  change  is  called 
limited  conversion,  and  we  see  that  a universal 
affirmative  proposition  when  so  converted 
gives  a particular  affirmative  one. 

67.  This  may  seem  all  very  plain  and  evident  when 
we  think  about  it  carefully,  yet  it  is  very  common  to 
meet  with  people  who  fall  into  mistakes  by  hasty 
and  careless  thinking.  By  frequently  seeing  animals, 
we  learn  that  they  are  all  capable  of  moving  them- 
selves in  some  way,  and  we  get  so  accustomed  to 
think  “all  animals  are  moving  things,”  that,  whenever 
we  see  a thing  moving  of  its  own  accord,  we  are 
inclined  to  infer  that  it  is  an  animal.  We  convert  the 
proposition  wrongly,  and  infer  that  “ all  moving  things 
are  animals.”  This  is  quite  untrue  ; for  not  only  are 
there  sensitive  plants,  fly-catchers,  sun-dews,  and  some 
other  large  plants,  which  move  almost  like  animals, 
but  there  is  an  immense  number  of  very  small  plants, 
visible  only  in  a good  microscope,  which  continually 
move  about  quite  as  quickly  as  small  animals.  It  is 
a curious  fact,  too,  that  very  small  particles  of  clay, 
mud,  glass,  or  sand,  when  put  into  pure  rain  water, 
and  examined  by  a strong  microscope,  are  found  to 
skip  about  as  quickly  as  insects. 

68.  It  is  not  unnatural,  however,  that  people  should 


IX.] 


PROPOSITIONS. 


SI 


sometimes  make  mistakes  in  converting  propositions 
of  the  universal  affirmative  kind,  because  in  not  a few 
cases  we  can  properly  convert  them  simply.  This 
is  certainly  the  case  when  the  subject  and  predicate 
are  singular  terms  (Art.  14).  Thus,  “The  Prince  of 
Wales  is  the  Duke  of  Cornwall,”  and  we  may  of 
course  convert  this  simply  into  “ The  Duke  of  Corn- 
wall is  the  Prince  of  Wales.”  The  poet  Pope  says, 
“ The  proper  study  of  mankind  is  man  ; ” but  we 
express  exactly  the  same  meaning  if  we  say,  “ man 
is  the  proper  study  of  mankind.” 

69.  In  other  cases  general  terms  may  exactly  co- 
incide one  with  another.  It  is  a truth  easily  proved  in 
geometry  that  all  triangles  with  three  equal  sides  have 
three  equal  angles ; at  the  same  time,  all  triangles 
with  three  equal  angles  have  three  equal  sides.  So 
that  we  might  express  the  two  truths  at  once,  by 
saying,  “ all  triangles  with  three  equal  sides  are  all 
triangles  with  three  equal  angles.”  This  wrould  be 
converted  simply  into  “ all  triangles  with  three  equal 
angles  are  all  triangles  with  three  equal  sides.” 
Whenever  we  meet,  then,  a proposition  stating  that 
one  thing  or  class  “is”  another,  or  agrees  with 
another,  we  ought  to  take  the  trouble  to  ascertain 
exactly  whether  the  subject  agrees  with  or  makes  the 
whole  of  the  predicate  or  only  part  of  it.  In  “all 
jelly  fish  are  animals,”  of  course  the  jelly  fish  are 
a small  part  only  of  the  animals  ; but  the  triangles 
with  three  equal  sides  exactly  agree  with  the  triangles 
with  three  equal  angles,  and  there  are  no  other 
triangles  with  three  equal  angles  except  those  which 
have  three  equal  sides. 

If  we  want  to  put  one  of  the  propositions  which 
we  have  just  been  considering  into  the  form  of  a 
circular  diagram,  a single  circle  will  suffice.  The 
circle  containing  “ man  ” ought  exactly  to  cover  and 
coincide  with  that  of  the  “ proper  study  of  mankind,” 


52 


PRIMER  OF  LOGIC. 


[ix. 


if  the  poet  Pope  be  correct.  This  is  shown  in 
Fig.  8. 


70.  There  is  yet  another  and  a rather  more  difficult 
way  of  converting  universal  affirmative  propositions. 
If  “all  coins  are  metallic,”  it  follows  that  “all  not- 
metallic  things  are  not  coins ; ” but  some  people 
appear  to  be  unable  to  see  at  first  sight  that  this 
follows.  A diagram,  however,  will  make  it  plain. 
In  Fig.  g,  all  metallic  things  are  supposed  to  be  inside 


the  larger  circle,  and  all  not-metallic  things  outside 
this  circle.  Now,  as  all  coins  are  within  the  smaller 
circle,  it  is  evident  that  none  of  the  not-metallic 
things,  which  are  outside  the  larger  circle  can  be 


X.] 


SYLLOGISM. 


53 


inside  the  smaller  circle.  Or,  we  may  explain  it  in 
this  way  : — -If  all  coins  are  metallic,  it  is  impossible 
that  what  is  not-metallic  should  be  a coin,  for  then 
it  would  be  also  metallic,  or  the  same  thing  would 
be  at  the  same  time  not-metallic  and  metallic,  which 
is  absurd.  From  every  universal  affirmative  pro- 
position we  may  then  infer  a new  proposition,  which 
has  the  negative  of  the  former  predicate  as  its  subject, 
and  the  negative  of  the  former  subject  as  its  pre- 
dicate. 

We  can  also  make  the  same  change  backwards ; 
from  “ all  not  useful  beings  are  not  living  beings/’ 
we  can  infer,  “ all  living  beings  are  useful  beings.” 
For  if  we  proceed  to  convert  this  last  proposition  in 
the  way  described,  we  get,  “ all  not  useful  beings  are 
not  living  beings,”  which  is  the  proposition  with 
which  we  began. 


X.— SYLLOGISM. 

71.  In  a great  many  of  the  arguments  which  we 
most  commonly  use,  one  proposition  is  gathered  or 
inferred  from  two  other  propositions.  It  is  well 
known,  for  instance,  that,  “ all  English  silver  coins  are 
coined  at  Tower  Hill,”  and  it  is  also  known  that,  “all 
sixpences  are  English  silver  coins.”  It  follows  that 
“all  sixpences  are  coined  at  Tower  Hill.”  These 
propositions  are  of  the  kind  called  universal  affirmative, 
but  we  may  give  different  names  to  them  nevertheless, 
according  to  the  place  they  hold  in  the  reasoning. 
That  last  proposition  which  we  gathered  from  the 
first  two  is  called  the  Conclusion,  probably  because 
the  argument  is  finished  when  we  have  learnt  what  it 
should  be.  The  other  two  propositions,  from  which 
we  gather  or  infer  the  conclusion,  are  called  pre- 
mises, because  they  are  put  forward,  or  put  first,  for 
the  purpose  of  being  reasoned  about. 


54 


PRIMER  OF  LOGIC. 


[x. 


72.  There  will  be  no  difficulty  in  seeing  why  the 
conclusion  follows  from  the  premises  in  the  case 
given.  For  one  premise  tells  us  that  “all  English 
silver  coins  are  among  those  coined  at  Tower  Hill,” 
though  they  are  not  the  whole,  as  gold  and  bronze 
coins  are  also  made  there.  The  other  premise  informs 
us  that  “all  sixpences  are  among  English  silver  coins,” 
sixpences  being  again  a part  only  of  such  silver  coins. 
If  we  take  three  circles  to  contain  respectively  six- 
pences, English  silver  coins,  and  things  coined  at 
Tower  Hill,  as  in  Fig.  10,  we  see  that  sixpences  are 


among  the  things  coined  at  Tower  Hill,  because  they 
are  among  the  English  silver  coins,  which  are  coined 
there. 

73.  As  a second  example  of  an  argument  in  which 
we  draw  one  proposition  from  two  others,  we  will  take 
the  following : — 

All  electors  pay  rates  ; 

N q paupers  pay  rates  ; 

Therefore,  no  paupers  are  electors. 

Here  the  conclusion  is  a universal  negative  one, 
and  it  is  inferred  from  two  premises,  the  first  of 
which  is  a universal  affirmative,  and  the  second  a 


X.] 


SYLLOGISM. 


55 


universal  negative  proposition.  We  may  explain  the 
reasoning  in  this  way  : all  electors  are  among  those 
who  pay  rates,  whereas  paupers  are  not  among  those 
who  pay  rates ; therefore  the  paupers  are  quite 
separated  from  the  electors.  Making  use  of  circles 
again,  we  see  that  the  circle  of  electors  is  inside  that 
of  those  who  pay  rates,  whereas  the  circle  of  paupers 
is  outside,  so  that  no  part  of  the  paupers’  circle  can 
touch  or  overlap  that  of  electors. 

74.  Although  in  these,  and  in  some  other  cases, 
it  is  very  easy  to  see  that  the  conclusion  will  follow 


from  the  premises,  this  is  not  always  the  case.  We 
must  therefore  examine  how  good  syllogisms  are  made 
up,  and  what  rules  we  must  obey  in  making  them. 
We  will  take  again  for  this  purpose  our  former  ex- 
ample : — 

All  English  silver  coins  are  coined  at  Tower  Hill ; 

All  sixpences  are  English  silver  coins  j 
Therefore  all  sixpences  are  coined  at  Tower  Hill. 

We  may  observe  that  there  are  only  three  terms  or 
classes  of  things  reasoned  about,  namely,  sixpences, 
English  silver  coins,  and  things  coined  at  Tower  Hill. 
Of  these,  the  class  of  English  silver  coins  does  not 
occur  in  the  conclusion  ; it  is  only  used  to  enable 


Fig.  11. 


56 


PRIMER  OF  LOGIC. 


[xr. 


us  to  compare  or  join  together  the  other  two  classes 
of  things,  and  in  the  diagram  (Fig.  io,  Art.  72)  its 
circle  lies  between  the  other  two  circles.  Accordingly, 
it  is  named  the  middle  term.  The  largest  circle 
is  that  containing  all  things  coined  at  Tower  Hill,  the 
predicate  of  the  conclusion,  and  this  is  called  the 
major  term  of  the  syllogism,  that  is  the  larger 
term.  Sixpences,  on  the  contrary,  being  in  the 
smallest  circle,  form  the  minor  or  the  lesser 
term,  which  is  always  the  subject  of  the  conclusion. 

75.  We  shall  have  a great  deal  to  do  with  major 
and  minor  and  middle  terms,  and  therefore  I must 
ask  the  learner  to  remember  carefully  that  the 
middle  term  is  always  the  term  which  is  not 
in  the  conclusion  ; that  the  major  term  is 
the  predicate  of  the  conclusion  ; and  that 
the  minor  term  is  the  subject  of  the  con- 
clusion. It  is  also  convenient  to  give  separate 
names  to  the  two  premises,  and  that  which  contains 
the  major  term  is  always  called  the  major  premise, 
and  that  which  contains  the  minor  term,  the  minor 
premise.  It  is  thought  to  be  more  correct  to  write 
the  major  premise  first,  but  even  if  it  be  put  second 
it  is  still  called  the  major  premise  because  it  con- 
tains the  major  term. 


XI.— THE  RULES  OF  THE  SYLLOGISM. 

76.  To  find  out  whether  an  argument  which  seems 
to  be  a syllogism  is  really  a syllogism,  we  must 
examine  it  carefully,  and  ascertain  whether  it  agrees 
with  certain  rules.  The  great  logician  Aristotle  more 
than  two  thousand  years  ago  discovered  these  rules 
and  showed  how  to  decide  when  supposed  syllogisms 
are  good,  and  when  they  are  not  good.  Several 
logicians  have  in  the  last  fifty  years  been  trying  to 


XI.] 


SYLLOGISM. 


57 


find  out  some  simpler  and  better  mode  of  ascertaining 
when  arguments  are  good,  but  they  have  not  yet 
agreed  upon  the  subject.  Until  they  do  agree  upon 
something  better,  we  shall  do  well  to  learn  the  old 
rules,  which  are  certainly  both  ingenious  and  useful. 

77.  Rule  I. — In  the  first  place  a syllogism  must 
contain  three  terms,  and  not  more  than  three 
terms  ; for  the  reasoning  consists  in  comparing  two 
terms  with  each  other  by  means  of  a third  term, 
which  we  have  called  the  middle  term.  If,  then, 
there  were  four  terms,  the  argument  would  consist 
either  of  two  syllogisms,  or  of  none  at  all.  Suppose 
the  terms  to  be  cow,  cloven-footed  animal,  ruminating 
animal,  and  animal  having  two  stomachs.  I may  say 
that  “all  cows  are  cloven-footed  animals,”  and  that 
“ all  ruminating  animals  have  two  stomachs ; ” but 
this  will  not  give  the  conclusion  “ all  cows  have  two 
stomachs,”  unless  we  have  yet  another  proposition 
comparing  cloven-footed  animals  with  ruminating 
animals.  But,  with  this  third  proposition,  we  can 
make  two  complete  syllogisms,  the  first  proving  that 
cows  are  ruminating  animals,  because  they  are  cloven- 
footed, and  all  cloven-footed  animals  are  ruminating 
animals ; and  the  second  in  like  manner  showing  that 
because  cows  are  ruminating  animals,  therefore  they 
have  two  stomachs. 

A syllogism  then  must  have  just  three  terms, 
neither  more  nor  less,  and  these  terms  are  called,  as 
we  have  already  learned  (Art.  74),  the  major,  middle, 
and  minor  terms. 

78.  Rule  II. — A syllogism  must  consist  of 
three  propositions,  and  only  three  proposi- 
tions, of  which  one  is  the  conclusion,  and  the  other 
two  are  the  major  and  minor  premises.  For  if  there 
be  four  propositions,  one  will  be  the  conclusion  and 
the  other  three  premises.  But  two  premises  are 
sufficient  to  compare  two  terms  with  a middle  term, 


PRIMER  OF  LOGIC. 


[XI. 


5S 


so  that  three  premises  will  either  make  no  such 
comparison  at  all,  or  will  make  two  syllogisms.  We 
may  easily  see  this  by  considering  again  the  case  of 
cows.  Two  propositions  enable  us  to  show  that  a 
cow  is  a ruminating  animal,  because  it  is  cloven- 
footed ; and  a third  proposition  enables  us  to  make 
a new  syllogism  showing  that  it  also  has  two 
stomachs. 

79.  Rule  III. — It  is  an  important  rule  that  the 
middle  term  of  a syllogism  must  be  distri- 
buted, that  is,  taken  universally,  or  in  its 
whole  extent  of  meaning,  once  at  least  in  the 
premises.  The  reason  for  this  rule  is  not  quite  so 
easy  to  explain,  but  it  will  afterwards  be  made  pretty 
evident  by  examples.  It  amounts  to  this,  that  unless 
we  take  the  whole  of  the  middle  term  once,  the  two 
premises  may  refer  to  different  parts  of  the  middle 
term,  so  that  there  may  really  be  no  true  middle  term 
at  all.  If  I say  that  “some  animals  are  flesh-eating 
animals,”  and  “ some  animals  have  two  stomachs,” 
it  would  be  absurd  to  infer  that  therefore  flesh-eating 
animals  have  two  stomachs.  The  “ some  animals  ” 
which  are  flesh-eating,  may  be,  and  in  fact  are,  quite 
distinct  from  the  other  “some  animals ” which  have 
two  stomachs.  We  may  in  fact  say  that  there  are 
four  terms,  and  that  we  thus  break  the  first  rule  of 
the  syllogism,  although  there  seem  to  be  only  three 
terms.  But  if  I argue  that,  because  “ some  animals 
are  flesh-eating,”  and  “ all  animals  consume  oxygen,” 
therefore  “ some  animals  consuming  oxygen  are  flesh- 
eating,” there  must  be  a good  middle  term.  The 
“ some  animals  ” in  the  major  premise  must  be  part 
of  the  “all  animals”  in  the  minor  premise,  and  thus 
we  have  a sure  means  of  comparison  between  the 
major  and  minor  terms. 

80.  Rule  IV. — This  rule  is  to  the  effect  that  we 
must  not  infer  anything  about  the  whole  of  a term, 


XI.] 


SYLLOGISM. 


59 


unless  something  was  said  about  the  whole  of  the 
term  in  the  premises.  In  other  words,  no  term 
must  be  distributed  in  the  conclusion  unless 
it  was  distributed  in  the  premises.  It  would 
be  absurd  to  argue  that  because  brittle  substances  are 
not  fit  for  coining,  and  some  metals  are  brittle  sub- 
stances, therefore  no  metals  are  fit  for  coining.  We 
can,  of  course,  infer  that  “ some  metals  ” are  not  fit 
for  coining,  namely,  those  which  are  brittle  ; but  to 
include  other  metals  as  well  is  simply  to  suppose  we 
have  knowledge  about  them  which  is  not  given  in  the 
premises  at  all.  It  is  not  always  so  easy  to  find  out 
when  this  rule  is  broken.  To  go  back  to  the  example 
in  Art.  79,  because  some  animals  eat  flesh,  and  all 
animals  consume  oxygen,  we  must  not  conclude  that 
all  which  consume  oxygen  eat  flesh.  We  must  re- 
member that  the  minor  premise,  “ all  animals  consume 
oxygen,”  is  an  affirmative  proposition,  which,  as  fully 
explained  in  Art.  55,  does  not  distribute  its  predicate, 
that  is,  does  not  refer  to  all  things  which  consume 
oxygen.  In  other  cases  the  way  in  which  this  fourth 
rule  is  broken  will  be  still  less  apparent  at  first  sight, 


but  these  cases  will  be  described  further  on  (Art.  87, 

88). 


6o 


PRIMER  OF  LOGIC. 


[xi. 


81.  Rule  V. — It  is  very  certain  that  from  two 
negative  premises  nothing  can  be  inferred. 

A negative  proposition  asserts  that  two  terms  differ, 
so  that  the  classes  of  things  denoted  by  the  terms  are 
wholly  or  partly  separated  from  each  other.  If  we 
say  then  that  no  Englishmen  are  slaves,  and  that 
no  negroes  are  Englishmen,  we  must  represent  the 
Englishmen  by  a circle  quite  separate  from  that  of 
the  slaves,  and  the  negroes  by  a circle  quite  separate 
from  that  of  Englishmen.  But  then  we  shall  see  after 
very  little  consideration  that  the  negroes’  circle  may 
be  placed  either  quite  away  from  that  of  the  slaves, 
or  may  be  made  to  overlap  it  more  or  less.  This 
means  that  negroes  may  be  not  slaves  at  all,  or  may 
be  partly  slaves  and  partly  not  slaves,  or  may  be 
all  slaves,  for  anything  which  the  two  premises  tell 
us  about  the  matter. 

82.  Rule  VI. — The  last  of  the  principal  rales  of 
the  syllogism  is  that,  if  one  premise  be  negative, 
the  conclusion  must  be  negative,  and  we 
cannot  get  a negative  conclusion  unless  one 
of  the  premises  be  negative.  We  may  perhaps 
see  the  truth  of  this  rule  most  easily  by  reflecting  that 
a negative  proposition  is  represented  by  one  circle 


outside  another.  Now,  if  we  say  all  negroes  are  dark, 
no  Englishmen  are  dark,  the  circle  of  negroes  is 
inside  that  of  dark  men,  while  that  of  Englishmen  is 


Fig.  13. 


XI.] 


SYLLOGISM. 


61 


outside,  so  that  the  circle  of  Englishmen  must  be 
outside  that  of  negroes,  giving  a negative  result.  It 
is  true  that  we  might  have  the  terms  differently 
arranged.  The  premises  might  be  all  negroes  are 
dark,  no  Chinese  are  negroes.  The  circle  of  negroes 


is  as  before  inside  that  of  dark  men  ; but  the  circle 
of  Chinese,  though  outside  that  of  negroes,  may  be 
wholly  inside  that  of  dark  men,  or  partly  inside  and 
partly  outside,  or  wholly  outside.  Such  premises  then 
tell  us  nothing  about  the  relative  position  of  Chinese 
and  negroes,  and  we  see  that  with  one  negative 
premise  we  either  get  a negative  conclusion,  or  no 
conclusion  at  all. 

83.  A second  part  of  the  rule  is  that  we  cannot 
get  a negative  conclusion  unless  one  premise  be 
negative.  We  may  satisfy  ourselves  that  this  is  true 
by  trying  with  circles  how  we  can  prove  one  circle 
to  be  outside  of  another  by  means  of  a third  circle. 
This  can  only  be  done  by  putting  one  inside  and  one 
outside  the  third  circle,  and  to  put  one  outside 
another  indicates,  as  we  have  often  seen,  a negative 
proposition. 

84.  Everyone  who  wishes  to  be  a good  logician 
must  remember  the  rules  of  the  syllogism  which  have 
now  been  described,  and  must  by  practice  become 

6 


6 2 


PRIMER  OF  LOGIC. 


[XI. 


quick  in  seeing  whether  an  argument  supposed  to  be 
a syllogism  does  or  does  not  obey  the  rules.  I will 
give  a few  more  examples  of  the  way  in  which  we 
must  examine  arguments  in  order  to  decide  whether 
they  are  good  syllogisms  or  not.  Do  the  following 
premises,  for  instance,  allow  of  the  conclusion  drawn 
from  them? — 

Every  city  contains  a cathedral. 

Liverpool  does  not  contain  a cathedral. 
Therefore,  Liverpool  is  not  a city. 

Here  the  middle  term,  or  that  which  does  not 
appear  in  the  conclusion,  is  “contain  (or  containing)  a 
cathedral.”  The  minor  term  is  Liverpool,  and  the 
major  term  city.  There  are  thus  three  terms  and  no 
more,  in  accordance  with  the  first  rule,  and  there  are 
three  propositions  and  no  more,  in  accordance  with 
the  second  rule.  The  third  rule  requires  that  the 
middle  term  shall  be  distributed,  or  taken  universally, 
once  at  least;  and  this  is  the  case,  because  the 
second  premise  “ Liverpool  does  not  contain  a cathe- 
dral” is  a negative  proposition,  and  therefore  dis- 
tributes its  predicate  (Art.  57).  As  to  the  fourth  rule, 
Liverpool  and  city  are  both  distributed  in  the  con- 
clusion, but  they  are  also  both  distributed  in  the 
premises,  so  that  the  rule  is  obeyed.  The  first  pre- 
mise is  affirmative,  so  that  the  fifth  rule  about  two 
negative  premises  cannot  be  broken.  The  sixth  rule 
is  likewise  obeyed,  which  requires  that  if  one  premise 
be  negative  the  conclusion  shall  be  so,  and  this  is  the 
case.  Thus,  the  argument  we  are  discussing  is  a 
perfectly  good  syllogism. 

85.  Let  us  next  examine  whether  the  following  pro- 
positions make  a syllogism  : — 

All  minerals  are  raised  from  mines. 

All  coals  are  raised  from  mines. 

Therefore,  all  coals  are  minerals. 


XI.] 


SYLLOGISM. 


6.5 


The  middle  term,  which  we  should  generally  look 
for  first,  is  “ raised  from  mines ; ” but  we  ought  to 
notice  at  once  that  both  the  propositions  in  which  it 
appears  are  affirmative.  Now  affirmative  propositions 
never  distribute  their  predicates  (Arts.  55,  59),  so  that 
the  third  rule  of  the  syllogism  is  broken,  which  re- 
quires that  the  middle  term  shall  be  distributed  once 
at  least.  In  this  case  there  is  said  to  be  a fallacy 
of  an  undistributed  middle  term. 

86.  This  was  the  kind  of  fallacy  into  which  an 
authoress  fell  when  she  wrote  a book  proving,  among 
other  things,  that  to  wear  false  hair  was  to  tell  a false- 
hood. In  reality  her  reasoning  came  to  this,  that  to 
wear  false  hair  was  to  deceive,  and  to  tell  a falsehood 
was  also  to  deceive.  But  the  predicate  to  deceive  is 
in  both  cases  particular  and  ought  to  be  explained  as 
meaning  one  way  of  deceiving.  Now  falsehood  is 
the  name  for  deceit  by  words,  and  is  not  the  proper 
name  for  deceit  by  other  means. 

To  make  a good  argument  out  of  this  matter  we 
ought  to  be  able  to  put  it  in  this  way  : — 

To  deceive  is  always  to  tell  a falsehood. 

To  wear  false  hair  is  to  deceive. 

Therefore,  to  wear  false  hair  is  to  tell  a falsehood. 

This  is  a perfectly  good  syllogism  supposing  it 
to  mean  that  every  case  of  deceiving  is  a case  of 
telling  a falsehood,  and  if  this  were  true  the  conclusion 
would  be  true.  But  it  is  evident  that  in  the  ordinary 
use  of  the  word  falsehood  the  first  premise  is  not  true. 
There  was  one  philosopher  who  tried  to  prove  in  like 
manner  that  whenever  a person  did  a wrong  act  it 
was  only  a particular  way  of  telling  a lie,  so  that  one 
who  killed  a fellow-creature  only  took  a round-about 
way  of  saying  that  he  was  not  a fellow-creature. 

87.  It  is  not  unnatural  that  people,  who  spend  their 


64 


PRIMER  OF  LOGIC. 


[XI. 


whole  lives  in  some  kind  of  study,  should  learn  to 
perceive  all  its  value,  while,  being  ignorant  of  other 
branches  of  learning,  they  cannot  so  readily  know  the 
value  of  those  branches.  Hence  they  are  likely  to 
fall  into  the  fallacy  of  arguing  that  because  their  own 
studies  are  very  useful  other  studies  are  not.  Let 
us  take  the  study  of  Latin  and  Greek  as  an  instance, 
and  compare  it  with  that  of  physical  science.  The 
argument  would  be  put  in  this  form  : — 

The  study  of  Greek  and  Latin  is  very  useful ; 

The  study  of  physical  science  is  not  the  study  of 
Greek  and  Latin  ; 

Therefore,  the  study  of  physical  science  is  not  very 
useful. 

In  this  argument  the  numbers  of  terms  and  pro- 
positions are  quite  correct,  and  at  the  first  moment 
it  may  not  be  easy  to  see  where  it  fails.  The  middle 
term,  or  that  which  does  not  appear  in  the  conclusion, 
is  “the  study  of  Greek  and  Latin.”  It  is  certainly 
distributed  in  the  second  premise  which  is  negative, 
and  may  also  be  said  to  be  distributed  in  the  first 
premise,  being  in  fact  a singular  term.  One  premise 
is  negative  and  the  conclusion  is  negative.  So  far 
all  is  right ; but  on  making  further  examination,  we 
shall  find  that  the  conclusion,  being  negative,  dis- 
tributes its  predicate  “ very  useful,”  while  the  first 
premise,  of  which  it  is  also  the  predicate,  does  not 
distribute  it.  Thus  the  supposed  argument  breaks 
the  fourth  rule,  that  no  term  shall  be  distributed  in 
the  conclusion  unless  it  were  distributed  in  one  of  the 
premises, 

88.  The  fact  is,  of  course,  that  there  may  be  a 
great  many  very  useful  studies,  and  because  the 
classical  studies  of  Greek  and  Latin  are  some  of  these, 
it  does  not  follow  that  other  ones  are  shut  out.  We 
may  show  this  most  clearly  by  a diagram  (Fig.  15), 


XI.] 


SYLLOGISM. 


65 


placing  the  several  studies  in  smaller  circles  enclosed 
in  the  larger  one  of  very  useful  studies.  The  circle 


Fig.  15 


of  Greek  and  Latin  must  be  distinct  from  that  of 
physical  science,  and  these  circles  must  not  over- 
lap each  other  at  all ; but  we  see  that  the  circle  of 
physical  science  may  nevertheless  be  placed  so  as  to 
be  wholly  within  that  of  “ very  useful  studies,”  or  partly 
within  and  partly  without,  or  wholly  without.  In  short, 
from  the  statement  that  Greek  and  Latin  are  very 
useful  subjects  of  study,  we  get  no  information  at 
all  as  to  whether  the  physical  sciences  are  or  are  not 
so.  We  may  say  the  same  of  the  study  of  mathe- 
matical, logical,  moral,  and  other  sciences.  None 
of  them  must  be  considered  useless,  because  the 
others  are  useful. 

89.  Suppose  I were  to  argue  that  all  householders 
pay  poor  rates,  and  all  electors  are  those  who  pay 
poor  rates  ; therefore,  all  householders  are  electors. 
Now,  as  a matter  of  fact,  it  is  true  according  to- the 
present  law  that  all  householders,  excepting  paupers, 
are  electors ; but  does  this  follow  from  the  pro- 
positions used  as  premises  to  reason  upon  ? The 
middle  term  seems  to  be  “ paying  poor  rates,”  and 


66 


PRIMER  OF  LOGIC. 


[xi. 


it  is  the  predicate  of  both  the  premises,  which  are 
affirmative.  Therefore  it  would  in  each  case  be 
undistributed,  and  by  the  third  rule  of  the  syllogism, 
the  argument  would  be  bad.  But  great  care  is  often 
required  in  examining  arguments,  and  in  reality  the 
second  proposition  is  not  what  we  took  it  to  be.  We 
do  not  simply  say,  “ all  electors  pay  poor  rates,”  or 
are  “ among  those  who  pay  poor  rates but  we  say 
that  they  “ are  ” those,  so  that  there  are  no  electors 
(in  ordinary  cases)  except  those  who  pay  poor  rates. 
This  is  one  of  those  propositions  (Art.  68)  which  we 
can  convert  simply,  so  that  we  may  state  it  as,  “all 
who  pay  poor  rates  are  (all)  electors ; ” and  as  all 
householders  pay  poor  rates,  excepting  paupers,  it 
follows  by  a good  syllogism,  that  all  householders  are 
electors. 

90.  There  are  two  minor  rules  of  the  syllogism 
which  we  may  deduce  from  the  rules  already  given. 
The  first  is  that  from  two  particular  propositions, 
whether  affirmative  or  negative,  we  cannot  deduce  any 
logical  conclusion.  Thus,  if  we  were  to  argue  that 
some  who  elect  members  of  Parliament  are  well- 
educated  men,  and  some  well-educated  men  are  per- 
fectly acquainted  with  what  the  country  needs,  we 
could  not  properly  infer  that  some  who  elect  members 
of  Parliament  are  perfectly  acquainted  with  what  the 
country  needs.  The  middle  term  is  “ well-educated 
men,”  and  it  is  the  predicate  of  the  first  of  the  pro- 
positions, so  that  it  is  undistributed.  It  is  also 
undistributed  as  the  subject  of  the  second  proposition, 
and  thus  what  seems  to  be  an  argument  breaks  the 
third  rule  of  the  syllogism.  As  we  may  explain  it, 
the  well-educated  men  who  elect  members  of  Parlia- 
ment might  happen  not  to  be  those  perfectly  ac- 
quainted with  what  the  country  needs.  In  the  same 
way,  if  we  were  to  take  other  examples  of  arguments 
containing  two  particular  propositions,  we  should  find 


XI.] 


SYLLOGISM. 


67 


that  they  can  never  give  a conclusion  according  to 
the  rules  of  the  syllogism. 

91.  A second  rule  which  follows  from  those  of  the 
syllogism  is  that,  if  either  premise  be  particular,  the 
conclusion  must  also  be  particular.  If  we  were  to 
argue  that  some  electors  are  not  fit  to  choose  good 
representatives,  but  all  well-educated  men  are  fit 
to  choose  good  representatives,  therefore  no  electors 
are  well-educated  men,  we  should  break  the  fourth 
rule  of  the  syllogism.  We  must  not  infer  anything 
at  all  about  all  electors,  when  in  the  first  proposition 
we  speak  only  of  some  electors.  In  a similar  way 
every  syllogism  in  which  one  premise  is  particular  and 
the  conclusion  is  not  particular  will  be  found  to  break 
one  rule  or  other  of  those  given  in  Arts.  77 — 82. 

92.  It  is  shown  in  almost  all  books  on  logic  that, 
when  we  try  in  how  many  different  ways  we  can  make 
syllogisms  with  each  of  the  four  kinds  of  propositions 
variously  put  together,  we  get  altogether  nineteen 
good  kinds  of  arguments,  called  the  nineteen 
moods  of  the  syllogism.  These  are  divided  into 
four  figures,  each  figure  being  known  by  the  position 
of  the  middle  term  in  the  premises.  Logicians  long 
ago  ascertained  in  what  cases  of  each  figure  a syl- 
logism is  valid,  and  they  recorded  the  results  in 
certain  curious  lines,  beginning  Barbara,  Celarent,  &c., 
which  were  so  constructed  that  the  vowels  in  each 
word  show  what  kinds  of  propositions  put  together 
in  a particular  way  will  make  a good  syllogism.  But 
it  is  not  of  much  advantage  to  know  these  lines  by 
heart,  because  we  ought  to  understand  the  rules  of 
the  syllogism  so  well  as  to  be  able  to  tell  in  every 
case  whether  an  argument  is  a correct  syllogism 
or  not. 

93.  Although  every  argument  which  is  a good 
syllogism  must  consist  of  two  premises  and  a con- 
clusion, these  three  propositions  will  not  usually  be 


68 


PRIMER  OF  LOGIC. 


[XI. 


stated  at  full  length.  People  sometimes  think  that 
they  are  not  arguing  by  syllogisms,  because  the  parts 
of  the  syllogisms  are  not  written  or  printed  exactly 
as  they  are  in  books  on  logic.  But  they  might  as 
reasonably  say  that  mental  arithmetic  is  not  arithmetic 
at  all,  because  the  sums  are  not  worked  out  at  full 
length  on  paper.  It  is  not  usual  to  state  more  than 
one  premise  of  a syllogism  in  addition  to  the  con- 
clusion, because  the  reader  can  then  judge,  without 
much  difficulty,  what  the  other  premise  is  intended 
to  be.  Thus  in  the  Sermon  on  the  Mount,  the  verses 
known  as  the  Beatitudes  consist  each  of  one  premise 
and  a conclusion,  and  the  conclusion  is  put  first. 
“ Blessed  are  the  merciful : for  they  shall  obtain 
mercy.”  The  subject  and  predicate  of  the  con- 
clusion are  here  inverted  (Art.  69),  so  that  the  pro- 
position is  really  “ The  merciful  are  blessed.”  It  is 
evidently  understood  that  “ All  who  shall  obtain  mercy 
are  blessed,”  so  that  the  syllogism,  when  stated  at 
full  length,  becomes  : — 

All  who  shall  obtain  mercy  are  blessed  ; 

All  who  are  merciful  shall  obtain  mercy; 
Therefore,  all  who  are  merciful  are  blessed. 

This  is  a perfectly  good  syllogism,  similar  to  those 
described  in  Arts.  10  and  74. 

94.  Wherever  any  one  of  the  words,  because, 
for,  therefore,  since,  or  other  words  used  in  the 
same  sense  occur,  we  may  be  sure  that  there  is  an 
argument,  and  in  many  cases  this  will  be  found  to 
be  a syllogism.  It  is  true  that  a great  many  of 
the  arguments  which  we  commonly  use  belong  rather 
to  geometrical  or  arithmetical  reasoning,  than  to 
simple  logic.  If  I were  to  argue,  for  instance,  that 
the  rocks  called  red  sandstone  lie  above  the  coal 
measures,  because  they  lie  above  the  Permian  rocks, 
which  lie  above  the  coal  measures,  this  is  perfectly 


XII.] 


HYPOTHETICAL  SYLLOGISMS. 


69 


good  reasoning.  But  it  is  not  merely  logical,  because 
it  deals  with  the  position  of  the  beds  of  rocks.  It 
is  a question  of  height,  and  belongs  to  geometry. 

XII.— HYPOTHETICAL  SYLLOGISMS. 

95.  It  was  stated  (Art.  51)  that  there  are  supposed 
to  be  three  kinds  of  propositions,  of  which  the  first 
and  most  common  kind  is  employed  in  the  syllogisms 
already  described.  We  must  not  overlook  hypo- 
thetical propositions  which  affirm  something  pro- 
vided or  “ if”  something  else  is  true.  By  joining  one 
such  proposition  with  an  ordinary  proposition  we  can 
make  a syllogism.  “ If  Manchester  contains  a cathe- 
dral it  is  a city;  but  Manchester  does  contain  a 
cathedral ; therefore,  it  is  a city.”  This  is  an  affirmative 
hypothetical  syllogism,  and  it  has  two  premises  and  a 
conclusion,  like  an  ordinary  syllogism.  The  first  pre- 
mise is  hypothetical  and  consists  of  two  parts,  the 
antecedent  containing  the  little  word  “if,”  and  the 
consequent  which  informs  us  what  will  happen  undei 
the  supposed  circumstances. 

96.  The  rules  of  this  kind  of  syllogism  are  very 
simple  : If  the  antecedent  be  affirmed,  the 
consequent  may  be  affirmed.  If  the  conse- 
quent be  denied,  the  antecedent  may  be 
denied.  In  the  instance  already  given  the  first  rule 
applies ; for  we  affirm  that  Manchester  does  contain  a 
cathedral,  and  then  affirm  the  consequence,  that  it  is 
a city.  As  an  example  of  the  second  rule,  we  may 
say,  “ If  the  atmosphere  were  equally  dense  at  all 
heights  there  could  be  no  perpetual  snow  on  the  Alps  ; 
but  there  is  perpetual  snow  on  the  Alps  : therefore,  the 
atmosphere  is  not  equally  dense.”  This  is  a negative 
hypothetical  syllogism. 

97.  We  must  take  much  care  not  to  fall  into 

the  fallacies  of  affirming  the  consequent,  or 


70 


PRIMER  OF  LOGIC. 


[XII. 


denying  the  antecedent,  and  imagining  that  we 
are  making  a good  syllogism.  It  would  be  wrong  to 
argue  that,  “ If  a man  is  a good  teacher,  he  thoroughly 
understands  his  subject ; but  John  Jones  thoroughly  un- 
derstands his  subject;  therefore,  he  is  a good  teacher.” 
The  conclusion  may  happen  to  be  true,  as  a matter  of 
fact,  but  it  does  not  follow  from  the  premises.  Nor 
can  we  argue  that,  “ If  snow  is  mixed  with  salt  it 
melts ; the  snow  on  the  ground  is  not  mixed  with 
salt  ; therefore  it  does  not  melt.”  This  argument  is 
obviously  absurd,  because  snow  melts  when  warmed, 
as  well  as  when  mixed  with  salt,  and  by  denying  the 
one  possible  antecedent  we  leave  other  possible  ones 
untouched. 

98.  In  reality,  however,  hypothetical  propositions 
and  syllogisms  are  not  different  from  those  which  we 
have  more  fully  considered.  It  is  all  a matter  of 
the  convenience  of  stating  the  propositions. 
Thus,  our  former  example  (Art.  95)  may  be  stated 
thus: — “All  towns  containing  cathedrals  are  cities; 
Manchester  is  a town  containing  a cathedral ; there- 
fore, Manchester  is  a city.”  This  is  a good  syllogism 
of  a very  common  kind,  the  middle  term  being  “ town 
containing  a cathedral.”  Our  second  example  is  not 
so  conveniently  stated  as  a common  syllogism,  but  we 
may  say,  “ An  equally  dense  atmosphere  is  not  an 
atmosphere  allowing  perpetual  snow  on  the  Alps ; 
but  our  atmosphere  is  one  allowing  perpetual  snow  on 
the  Alps : therefore,  our  atmosphere  is  not  an  equally 
dense  atmosphere.”  This  is  a good  syllogism  with  a 
negative  major  premise  and  a negative  conclusion, 
and  all  the  other  hypothetical  syllogisms  can  be  turned 
into  ordinary  ones  in  the  way  shown  by  one  example 
or  the  other. 

99.  We  can  now  see  that  to  affirm  the  conse- 
quent and  then  to  infer  that  we  can  affirm 
the  antecedent,  is  as  bad  as  breaking  the 


XIII.] 


ARGUMENTS. 


7i 


third  rule  of  the  syllogism,  and  allowing  an 
undistributed  middle  term.  This  is  very  evident  in 
the  example  given  (Art  97)  which  becomes,  “A  good 
teacher  thoroughly  understands  his  subject;  John 
Jones  thoroughly  understands  his  subject;  therefore, 
John  Jones  is  a good  teacher.”  Both  the  premises  being 
affirmative  and  having  the  middle  term  “ thoroughly 
understands  his  subject”  for  their  predicate,  it  follows 
that  the  middle  term  is  not  distributed  in  either  pre- 
mise. 

To  deny  the  antecedent  is  really  to  break 
the  fourth  rule  of  the  syllogism,  and  to  take 
a term  as  distributed  in  the  conclusion  which  was 
not  so  in  the  premise.  Instead  of  saying,  “ If  snow  is 
mixed  with  salt  it  melts  ” we  may  say  more  simply, 
“ Snow  mixed  with  salt  melts ; but  the  snow  on  the 
ground  is  not  mixed  with  salt;  therefore,  it  does  not 
melt.”  Here  the  conclusion  is  negative,  and  therefore 
distributes  its  predicate  “melts”  or  “melting.”  But 
this  term  occurs  as  the  predicate  of  the  first  premise, 
which  is  affirmative,  so  that  it  is  not  distributed,  break- 
ing the  fourth  rule  of  the  syllogism.  This  example  is 
exactly  like  that  given  in  Article  87. 

XIII. — OTHER  KINDS  OF  ARGUMENTS. 

100.  It  would  be  quite  a mistake  to  suppose  that 
all  good  logical  arguments  must  obey  the  rules  of  the 
syllogism,  which  we  have  been  considering.  Only 
those  arguments  which  connect  two  terms  together  by 
means  of  a middle  term,  and  are  therefore  syllogisms, 
need  obey  these  rules.  A great  many  of  the  arguments 
which  we  daily  use  are  of  this  nature  ; but  there  are 
a great  many  other  kinds  of  arguments,  some  of  which 
have  never  been  understood  by  logicians  until  recent 
years. 

101.  One  important  kind  of  argument  is  known  as 


7- 


PRIMER  OF  LOGIC. 


[xm. 


the  disjunctive  syllogism,  though  it  does  not  obey 
the  rules  of  the  syllogism,  or  in  any  way  resemble 
syllogisms.  We  learned  (Art.  52)  that  disjunctive 
propositions  are  those  which  have  several  terms  joined 
together  by  the  little  word  “ or.”  We  use  such  pro- 
positions when  we  divide  up  a class  into  smaller 
classes ; thus  we  may  say,  speaking  without  scientific 
accuracy,  that  a vegetable  is  either  a tree,  or  a shrub, 
or  a herb.  A boat  is  either  a sailing-boat,  or  a row- 
boat, or  a steam-boat.  The  metal  of  which  money  is 
made  is  either  gold,  or  silver,  or  copper,  or  bronze,  or 
nickel.  There  may  be  any  number  of  things  thus 
stated  ; for  instance,  a member  of  the  House  of 
Commons  must  be  either  Mr.  Disraeli,  or  Mr.  Glad- 
stone, or  Mr.  Forster,  or  Sir  Stafford  -Northcote,  or 
any  one  of  about  650  other  men  who  belong  to  the 
House.  Each  of  the  things  or  smaller  classes  thus 
joined  together  by  “ or  ” will  be  called  alternatives, 
because  we  may  take  our  choice  between  them,  and 
if  one  will  not  do  another  may  do. 

ro2.  The  principal  rule  according  to  which  we  use 
disjunctive  propositions  in  arguments  is  that  if  one 
or  more  alternatives  be  denied  the  rest  may 
be  affirmed.  Thus  fuel  consists  of  carbon  or 
hydrogen.  If  then  any  particular  portion  of  fuel 
does  not  consist  of  hydrogen,  it  must  consist  of  carbon. 
Here  there  are  only  two  alternatives,  and  in  this  and 
a great  many  like  cases,  if  we  deny  one  alternative  we 
must  affirm  the  only  remaining  one.  A crime  is  either 
treason,  or  felony,  or  misdemeanour.  Forgery  is  not 
treason  nor  misdemeanour;  therefore,  it  is  felony. 
Here  we  have  three  alternatives,  two  of  which  are 
denied,  so  that  the  other  one  alone  remains  to  be 
affirmed.  Roofing  materials  are  either  slates,  or  thatch, 
or  shingles,  or  iron,  or  tiles,  or  felt,  or  paper.  Here 
we  have  seven  alternatives,  and,  if  we  held  them  to 
be  all  the  existing  ones,  it  would  follow  that  a house 


XIV.] 


RULE  OF  INFERENCE. 


73 


not  roofed  with  slates  or  thatch  must  be  roofed  with 
shingles,  or  iron,  or  tiles,  or  felt,  or  paper.  These 
disjunctive  arguments,  it  will  be  seen,  may  be  very 
various  in  the  number  of  alternatives  denied  and 
affirmed ; but  they  none  of  them  obey  the  rules  of  the 
syllogism,  because  one  proposition  is  always  negative 
and  yet  the  conclusion  is  affirmative,  which  is  against 
the  sixth  rule  (Art.  82). 

103.  It  is  said  in  some  books  on  logic  that,  if  we 
affirm  one  alternative  of  a disjunctive  proposition,  we 
must  deny  the  remainder.  It  would  be  said,  for 
instance,  that  as  fuel  is  composed  of  carbon  or  of 
hydrogen,  what  fuel  is  composed  of  carbon  is  not 
composed  of  hydrogen.  But  this  is  not  true,  because 
nearly  all  fuel  • is  composed  of  both  substances  at  the 
same  time.  Again,  it  might  be  inferred  that,  as  boats 
are  either  sailing-boats,  or  row-boats,  or  steam-boats, 
therefore  a boat  which  is  a steam -boat  is  not  a sailing- 
boat,  nor  a row-boat.  But  this  need  not  be  so,  and 
most  steam-boats  are  able  to  set  sails,  when  it  is 
desirable  or  necessary  to  do  so.  A magistrate  is  a 
justice  of  the  peace,  or  a mayor,  or  a stipendiary 
magistrate  ; but  it  does  not  follow  that  one  who  is  a 
justice  of  the  peace  is  not  a mayor.  After  affirming 
one  alternative  we  ctm  only  deny  the  others  if  there 
be  such  a difference  between  them  that  they  could 
not  be  true  at  the  same  time. 

XIV.— THE  GREAT  RULE  OF  INFERENCE. 

104.  There  is  a simple  rule  which  will  enable  us  to 
test  the  truth  of  a great  many  arguments,  even  of 
many  which  do  not  come  under  any  of  the  rules  com- 
monly given  in  books  on  logic.  This  rule  is  that 

whatever  is  true  of  one  term  is  true  of  any 
term  which  is  stated  to  be  the  same  in  mean- 
ing as  that  term.  In  other  words,  we  may  always 
7 


74 


PRIMER  OF  LOGIC. 


[xiv. 


substitute  one  term  for  another  if  we  know 
that  they  refer  to  exactly  the  same  things. 

There  is  no  doubt  that  a horse  is  some  animal, and  there- 
fore the  head  of  a horse  is  the  head  of  some  animal. 
This  argument  cannot  be  brought  under  the  rules  of 
the  syllogism,  because  it  contains  four  different  logical 
terms  in  two  propositions,  namely,  horse,  some  animal, 
head  of  horse,  head  of  some  animal.  But  it  easily 
comes  under  the  rule  which  I have  given,  because  we 
have  simply  to  put  “ some  animal  ” instead  of  “ a 
horse.”  A very  great  number  of  arguments  may  be 
explained  in  this  way.  Gold  is  a metal ; therefore,  a 
piece  of  gold  is  a piece  of  metal.  A negro  is  a 
fellow  creature  ; therefore,  he  who  strikes  a negro, 
strikes  a fellow  creature.  A domestic  animal  is  a 
creature  capable  of  suffering ; therefore,  he  who  ill- 
treats  a domestic  animal,  ill-treats  a creature  capable 
of  suffering. 

105.  Let  it  be  carefully  remarked  that  in  an  ordinary 
universal  affirmative  proposition,  like,  “ A negro  is  a 
fellow  creature,”  we  cannot  put  negro  simply  for 
fellow  creature.  It  would  be  absurd  to  argue  that, 
because  a man  strikes  a fellow  creature,  therefore  he 
strikes  a negro.  This  is  evidently  because  negroes 
form  only  a part  of  our  fellow  creatures.  But  in  other 
cases,  as  already  mentioned  (Art.  69),  the  subject  and 
predicate  of  a proposition  refer  to  exactly  the  same 
numbers  of  objects,  and  altogether  coincide.  All 
parallelograms,  for  instance,  are  all  plane  four-sided 
figures,  whose  opposite  angles  are  equal.  It  follows 
that  whatever  we  know  of  a four -sided  figure  of  this 
description  is  true  of  a parallelogram,  and  whatevc  r 
we  know  of  parallelograms  is  true  of  such  figures. 
Any  figure  which  has  not  its  opposite  angles  equal 
cannot  be  a parallelogram.  When  the  terms  of  a 
proposition  are  singular  ones,  this  is  still  more  evident. 
The  moon  is  the  earth’s  satellite ; it  follows  that  any- 


XIV.] 


RULE  OF  INFERENCE. 


75 


thing  which  is  true  of  the  earth’s  satellite  is  true  of 
the  moon ; and  anything  which  is  true  of  the  moon  is 
true  of  the  earth’s  satellite.  The  moon,  as  far  as  we 
can  learn,  is  without  an  atmosphere,  and  without  seas  ; 
therefore  the  earth’s  satellite  is  without  an  atmosphere 
and  without  seas. 

106.  It  is  really  in  the  same  way  that  we  argue 
about  quantities.  Thus  the  length  of  Westminster 
Abbey  is  505  feet ; therefore,  anything  true  of  505  feet 
is  true  of  the  length  of  Westminster  Abbey.  The 
length  of  Canterbury  Cathedral  is  greater  than  505 
feet  by  9 feet ; therefore  it  is  greater  than  that  of 
Westminster  Abbey  by  9 feet  The  width  of  Bristol 
Cathedral  is  equal  to  that  of  Bath  Abbey  Church. 
Hence  it  follows  that,  in  respect  to  width,  we  can 
always  put  Bristol  Cathedral  for  the  Bath  Abbey 
Church,  or  the  latter  for  the  former.  It  happens,  for 
instance,  that  the  width  of  St.  Mary’s  Church,  at 
Redcliffe,  Bristol,  is  less  than  that  of  the  Cathedral ; 
hence  it  follows  that  it  is  less  than  that  of  the  Bath 
Abbey  Church.  On  the  other  hand,  Exeter  Cathedral 
has  by  accident  the  same  width  as  Bristol  Cathedral ; 
therefore,  putting  the  Bath  Abbey  Church  for  Bristol 
Cathedral,  we  find  that  the  Cathedral  of  Exeter  and 
the  Bath  Abbey  Church  have  the  same  width. 

107.  When  we  examine  carefully  enough  the  way 
in  which  we  reason,  it  will  be  found  in  every  case 
to  consist  in  putting  one  thing  or  term  in 
place  of  another,  to  which  we  know  it  to 
have  an  exact  resemblance  in  some  respect. 
We  use  the  likeness  as  a kind  of  bridge,  which  leads 
us  from  a knowledge  of  one  thing  to  a knowledge 
of  another;  thus  the  true  principle  of  reasoning 
may  be  called  the  substitution  of  similars, 
or  the  passing  from  like  to  like.  We  infer  the 
character  of  one  thing  from  the  character  of  some- 
thing which  acts  as  a go-between,  or  third  term. 


76 


PRIMER  OF  LOGIC. 


[xv. 


When  we  are  certain  there  is  an  exact  likeness,  our 
inference  is  certain ; when  we  only  believe  that  there 
probably  is,  or  guess  that  there  is,,  then  our  inferences 
are  only  probable,  not  certain. 

XV.— INDUCTIVE  REASONING. 

10S.  In  all  the  preceding  parts  of  this  Primer  we 
have  been  inquiring  how  we  may  gather  the  truth 
contained  in  some  propositions,  called  Premises,  and 
put  it  into  another  proposition,  called  the  Conclusion. 
We  have  not  yet  undertaken  to  find  out  how  we  can 
learn  what  propositions  really  are  true,  but  only 
what  propositions  are  true  when  other  ones 
are  true.  All  the  acts  of  reasoning  yet  considered 
woald  be  called  deductive,  because  we  deduce, 
or  lead  down  the  truth  from  premises  to  con- 
clusion. It  is  an  exceedingly  important  thing  to 
understand  deductive  inference  correctly,  but  it  might 
seem  to  be  still  more  important  to  understand  induc- 
tive inference,  by  which  we  gather  the  truth  of 
general  propositions  from  facts  observed  as  happening 
in  the  world  around  us. 

109.  It  ought  to  be  easy  to  see  that  reasoning  alone 
will  never  teach  us  anything,  because  it  only  gives  us 
one  proposition,  when  we  already  have  other  ones. 
How  then  are  we  to  get  the  original  propositions  ? 
This  must  be  done  by  using  our  eyes  and  ears,  and 
observing  things  about  us,  so  as  to  leam  what  they 
really  are.  How  are  we  to  know  that  all  very  small 
particles  of  water  in  daylight  appear  white,  except  by 
examining  the  appearance  of  clouds,  mist,  foam,  spray, 
steam,  and  any  other  things  which  we  know  to  be 
composed  of  small  particles  of  water?  This  seems 
to  be  evidently  the  proper  way  to  get  knowledge,  and 
we  may  well  wonder  that  people  ever  thought  differ- 
ently. Nevertheless,  for  many  centuries  it  was  believed 


XV.] 


INDUCTIVE  REASONING. 


77 


to  be  possible  to  arrive  at  all  necessary  knowledge  by 
the  use  of  the  syllogism,  and  men  preferred  trusting 
to  Aristotle,  rather  than  using  their  own  eyes. 

no.  The  rise  of  modern  science  may  perhaps  be 
considered  to  date  as  far  back  as  the  time  of  Roger 
Bacon,  the  wonderful  monk  and  philosopher  of  Oxford, 
who  lived  between  the  years  1214  and  1292.  He 
was  probably  the  first  in  the  middle  ages  to  assert 
that  we  must  learn  science  by  observing  and  experi- 
menting on  the  things  around  us,  and  he  himself 
made  many  remarkable  discoveries.  Galileo,  however, 
who  lived  more  than  300  years  later  (1564  to  1642), 
was  the  greatest  of  several  great  men,  who  in  Italy, 
France,  Germany,  or  England,  began  by  degrees  to 
show  how  many  important  truths  could  be  discovered 
by  well-directed  observation.  Before  the  time  of 
Galileo,  learned  men  believed  that  large  bodies  fall 
more  rapidly  towards  the  earth  than  small  ones, 
because  Aristotle  said  so.  But  Galileo,  going  to  the 
top  of  the  Leaning  Tower  of  Pisa,  let  fall  two  un- 
equal stones,  and  proved  to  some  friends,  whom  he 
had  brought  there  to  see  his  experiment,  that  Aristotle 
was  in  error.  It  is  Galileo’s  spirit  of  going 
direct  to  Nature,  and  verifying  our  opinions 
and  theories  by  experiment,  that  has  led  to 
all  the  great  discoveries  of  modern  science. 

hi.  People  very  commonly  believe  that  Francis 
Bacpn,  usually  called  Lord  Bacon,  who  lived  between 
the  years  1561  and  1629,  was  the  founder  of  inductive 
logic  and  of  true  scientific  method.  It  is  quite  certain 
that  Lord  Bacon  was  an  exceedingly  clever  man,  and 
in  many  ways  a great  man.  In  his  celebrated  work, 
the  Novum  Organum,  or  the  New  Instrument, 
he  strongly  points  out  the  need  of  observing  Nature 
and  collecting  a great  many  facts,  from  which  general 
laws  might  gradually  be  collected,  and  he  foresaw  that 
valuable  discoveries  would  be  made.  But  it  is  quite  a 


PRIMER  OF  LOGIC. 


[xv„ 


78 


mistake  to  suppose  that  Lord  Bacon  really  understood 
the  inductive  logic  by  which  Galileo,  about  the  same 
time,  and  Sir  Isaac  Newton  and  other  great  men  after 
him,  succeeded  in  detecting  the  chief  laws  of  nature. 
Not  only  was  Lord  Bacon  unable  to  make  any 
real  discoveries  by  his  own  methods  of  inquiry,  when 
he  tried  to  do  so,  but  he  could  not  see  the  truth  of 
the  excellent  discoveries  in  astronomy  and  magnetism, 
which  Copernicus,  and  an  Englishman  named  Gilbert, 
had  made  known  a little  time  before.  Thus  it  is 
wrong  to  speak  of  Lord  Bacon’s  philosophy  as  if  his 
book  the  Novum  Organum  really  taught  men  how  to 
investigate  nature,  and  if  we  continue  to  speak  of 
Bacon’s  Philosophy,  meaning  the  new  inductive  logic, 
we  ought  to  attribute  it  to  Roger  Bacon 
rather  than  to  Lord  Bacon. 

1 1 2.  Inductive  logic  inquires  by  what  man- 
ner of  reasoning  we  can  gather  the  laws  of 
nature  from  the  facts  and  events  observed. 
Such  reasoning  is  called  induction,  or  inductive 
inquiry,  and,  as  it  has  actually  been  practised  by  all 
the  greatest  discoverers  in  science,  it  consists  in  four 
steps. 

1 13.  In  the  first  place,  we  must  gain,  by  almost 
accidental  observations  and  experiments,  a knowledge 
of  facts  touching  the  subject  of  inquiry.  Such  know- 
ledge of  mere  facts  is  not  properly  called  science  at 
all,  because  the  facts  are  disconnected,  and  do  not 
enable  us  to  explain  other  facts,  or  to  discover  what 
will  happen  before  we  have  tried  the  experiment.  It 
is  merely  knowledge  given  by  the  senses. 

1 14.  In  taking  the  second  step,  we  proceed  to 
reason  about  these  facts,  which  we  do  by  inventing 
or  imagining  laws,  which  may  be  true  of  the  things 
examined.  We  make  what  is  called  an  hypothesis 
and  suppose  some  law  or  general  proposition  to  be 
true  for  the  sake  of  argument.  We  see  now  why 


INDUCTIVE  REASONING. 


79 


xv.] 

deductive  logic  is  so  very  important,  because  it  is 
only  by  deductive  reasoning  that  we  can  tell  what  will 
be  the  consequences  of  the  law  or  proposition  sup- 
posed. 

1 1 5.  In  the  third  step,  then,  we  reason  by  the 
syllogism,  or  by  other  kinds  of  deductive  argument, 
to  the  particular  facts  which  will  be  true  if  the  hypo- 
thesis be  true. 

1 1 6.  In  the  fourth  step,  we  proceed  to  compare 
these  deductions  with  the  facts  already  collected,  or, 
when  necessary  and  practicable,  we  make  new  observa- 
tions and  plan  new  experiments,  so  as  to  find  out 
whether  the  hypothesis  agrees  with  nature.  If  we 
meet  with  several  distinct  disagreements  between  our 
deductions  and  our  observations,  it  will  become  likely 
that  the  hypothesis  is  wrong,  and  we  must  then  invent 
a new  one.  In  order  to  produce  agreement  it  will 
sometimes  be  enough  to  change  the  hypothesis  in  a 
small  degree. 

1 1 7.  When  we  get  hold  of  an  hypothesis  which 
seems  to  give  results  agreeing  with  a few  facts,  we 
must  not  at  once  assume  that  it  is  certainly  correct. 
We  must  go  on  making  other  deductions  from  it  under 
various  circumstances,  and,  whenever  it  is  possible,  we 
ought  to  verify  these  results,  that  is  compare  them 
with  facts  observed  through  the  senses.  When  an 
hypothesis  is  shown  in  this  way  to  be  true  in  a great 
many  of  its  results,  especially  when  it  enables  us 
to  predict  what  we  should  never  otherwise  have 
believed  or  discovered,  it  becomes  almost  certain  that 
the  hypothesis  itself  is  a true  one. 

1 18.  Thus  there  may  be  said  to  be  four  different 
steps  in  inductive  reasoning  : — 

First  Step. — Preliminary  observation. 

Second  Step. — The  making  of  hypotheses. 

Third  Step. — Deductive  reasoning. 

Fourth  Step. — Verification. 


So  PRIMER  OF  LOGIC.  [xv. 

I will  now  proceed  to  show  by  examples  that  it 
is  really  by  this  mode  of  reasoning  in  four  successive 
steps  that  we  learn  the  nature  of  things,  and  thus 
become  able  to  make  true  general  propositions  about 
them. 

1 1 9.  Hundreds  of  years  ago  people  had  frequently 
noticed  in  stones  and  on  the  face  of  exposed  rocks, 
peculiar  forms  closely  resembling  those  of  living 
animals,  shells,  or  plants.  These  fossils  were  so  re- 
markable that,  though  observed  by  mere  accident, 
people  could  not  help  forming  hypotheses  to  explain 
the  resemblance  to  living  beings,  and  very  different 
these  hypotheses  were.  The  favourite  one  was  that 
the  Great  Deluge  carried  shells,  drowned  animals,  and 
other  things  about,  and  in  retreating  left  them  scattered 
over  the  surface  of  the  earth,  even  upon  the  tops  of 
high  mountains.  The  celebrated  Voltaire,  on  the 
contrary,  suggested  that  the  shells  found  high  up  in 
the  Alps  must  have  been  dropped  by  the  pilgrims, 
who  used  to  cross  the  mountains  in  former  centuries. 
Perhaps  a more  reasonable  hypothesis  was  to  the 
effect  that  they  were  “ freaks  of  nature,”  that  is,  that 
the  resemblance  to  animals  and  plants  arose  from 
accident,  just  as  frost  on  a window-pane  sometimes 
resembles  the  branches  of  a tree.  A further  hypo- 
thesis was  that  the  fossils  really  consisted  of  the  remains 
of  living  beings  covered  up  in  the  mud  or  sand  which 
became  the  substance  of  rocks  innumerable  centuries 
ago.  The  last  hypothesis  was  selected  as  the  true 
one  by  the  processes  of  deductive  reasoning  and 
verification,  which  I have  described. 

120.  We  proceed  to  reason  about  the  hypotheses 
somewhat  in  this  way.  If  the  Great  Deluge  deposited 
the  fossils  on  mountains,  then  the  fossils  ought  to  be 
found  only  on  the  surface  or  near  it,  whereas  great 
numbers  of  fossils  are  found  in  deep  mines,  driven 
through  hard  rocks,  where  the  waters  of  the  Deluge 


XV.] 


INDUCTIVE  REASONING. 


cannot  have  placed  them.  This  hypothesis,  therefore, 
is  wrong.  Nor  is  that  of  Voltaire  any  better ; for 
fossils  are  found  on  mountains,  and  in  parts  of  the 
earth,  the  Arctic  Regions  for  instance,  where  pilgrims 
never  went,  not  to  speak  of  the  fossils  sunk  deep  in 
the  earth.  The  hypothesis  about  “freaks  of  nature” 
is  less  easy  to  disprove,  and  there  is  no  doubt  that  at 
various  times,  things  have  been  believed  to  be  fossil 
remains  of  animals  and  plants  which  were  not  so. 
But  we  may  argue  in  this  way  : if.  in  such  a great 
multitude  of  cases,  stones  have  been  formed  by  mere 
accident  in  the  shapes  of  living  things,  there  is  equal 
reason  why  they  should  take  by  accident  the  forms  of 
other  objects.  Why  should  we  not  meet  with  fossil 
books,  and  fossil  teapots,  and  fossil  chairs  and  tables  ? 
The  hypothesis  of  freaks  of  nature  does  not  give 
any  reason  to  expect  what  we  do  find,  more  than 
multitudes  of  things  which  we  do  not  find. 

i2i.  The  last  hypothesis,  on  the  contrary,  namely, 
that  an  immense  number  of  animals  and  plants  have 
lived  in  past  ages,  and  left  their  remains  buried  in  the 
strata  of  sand  and  mud  then  deposited  in  the  seas, 
lakes,  or  rivers,  enables  us  to  explain  many  peculiar 
facts.  We  see  how  it  is  possible  that  these  remains 
should  be  found  at  great  depths  in  the  crust  of  the 
earth,  one  layer  of  rock  after  another  having  been 
formed  during  many  millions  of  years.  We  can  argue 
in  this  way  too  : if  an  animal  be  buried  in  the  earth 
at  the  present  day,  we  know  that  the  flesh  and  soft 
parts  will  quickly  disappear,  and  after  the  lapse  of  a 
hundred  years  only  the  bones,  teeth,  and  hard  parts 
will  remain.  Accordingly,  if  animals  with  skeletons 
lived  in  former  geological  ages,  we  ought  usually  to 
find  only  the  bones  and  durable  parts.  And  it  is  a 
fact  that  we  possess  the  fossil  skeletons  of  multitudes 
of  animals  whose  forms  are  otherwise  unknown  to  us. 
We  meet  too  with  the  shells  of  shell-fish,  the  hard 


82 


PRIMER  OF  LOGIC. 


[xv. 


scales  of  fishes  or  reptiles,  the  bark  of  trees,  in  short 
just  those  parts  which  are  most  durable.  Sometimes 
even  the  bones  of  an  animal  have  been  wholly  rotted 
away,  and  yet  the  teeth,  which  are  the  hardest  and 
most  indestructible  parts  of  the  whole  body,  remain. 

122.  We  can  argue,  again,  that  if  shell-fish  were 
embedded  in  mud  and  then  pressed  with  an  immense 
weight  of  rock  gradually  formed  over  them,  they  ought 
to  be  compressed  and  flattened.  Accordingly  we  do 
find  fossil  shells  sometimes  quite  flat  and  broken  as  if 
by  pressure,  and  the  remains  of  the  trunks  of  trees 
discovered  in  coal  mines  are  never  quite  round,  but 
partially  flattened.  In  these  and  many  other  ways, 
then,  we  can  argue  that  if  animals  and  plants 
did  live  millions  of  years  ago,  their  remains 
would  now  present  appearances  which  agree 
with  what  is  observed.  Hence  we  are  obliged 
to  reject  all  the  previous  hypotheses,  which  disagreed 
with  facts,  and  adopt  the  last  hypothesis  which  so  well 
agrees. 

123.  Probably  the  most  important  law  of  nature 
ever  discovered  is  that  called  the  Law  of  Gravity, 
which  states  that  all  bodies  in  space  tend  to  fall 
towards  each  other  with  a certain  force  depending  on 
the  magnitudes  of  the  bodies  and  the  distance  between 
them.  It  might  seem  that  we  need  no  aid  of  logic  to 
show  us  that  things  fall  towards  the  earth,  because, 
whether  we  throw  up  a stone  or  a book,  a gold  coin 
or  a feather,  they  will  all  descend  more  or  less  quickly 
to  the  surface  of  the  earth.  The  ancient  Greeks 
observed  this  much,  and  no  doubt  the  ancient  Egyp- 
tians and  other  peoples  before  them.  But  then  it 
does  not  seem  to  be  true  that  all  bodies  fall ; for 
flames  ascend  upwards,  and  in  smoke,  and  clouds,  and 
bubbles  we  have  other  exceptions.  Aristotle,  the 
greatest  of  Greek  philosophers,  came  to  the  conclusion 
that  some  things  were  naturally  heavy  and  tended  to 


XV.] 


INDUCTIVE  REASONING. 


fall,  while  other  things  were  naturally  light,  and  tended 
to  rise.  Only  about  two  hundred  years  ago  did 
Newton  succeed  in  showing  how  much  better  it  was 
to  make  the  hypothesis  that  all  things  tend  to  fall, 
because  he  could  then  explain  not  only  the  motions 
of  flame  and  other  apparently  light  things,  but  also 
the  movements  of  the  moon,  sun,  and  planets.  If 
we  put  a pound  weight  into  one  scale  of  a balance, 
and  only  half-a-pound  into  the  other  scale,  the  latter 
will  of  course  go  up  as  the  former  is  pulled  down  by 
the  greater  force.  So,  if  flame  be  a lighter  substance 
than  the  air  around,  it  will  be  forced  or  buoyed  up 
like  a cork  in  water.  Thus,  when  we  argue  deduc- 
tively, we  find  that  what  is  apparently  tending  to  rise 
upwards  may  really  be  tending  to  fall  downwards,  but 
is  overpowered  by  the  greater  tendency  of  other 
bodies. 

124.  Newton  argued  again  in  this  way:  if  all 
bodies  tend  to  fall  towards  each  other,  all  bodies 
ought  to  fall  towards  the  earth.  Now  the  moon  is  a 
body,  and  therefore  it  ought,  according  to  evident 
reasoning  in  the  manner  of  the  syllogism,  to  fall 
towards  the  earth.  Why  does  it  not  do  so,  but  go  on 
revolving  round  the  earth  once  in  every  lunar  month  ? 
It  occurred  to  him  that,  if  the  moon  were  not  in  some 
way  held  by  the  earth,  it  ought  to  go  off  flying  away 
in  a straight  line  like  a stone  from  a rapidly  revolving 
sling.  A moving  body  will  move  in  a straight  line 
unless  some  force  obliges  it  to  alter  its  course.  Thus 
it  appeared  likely  that  in  reality  the  moon  was  always 
falling  towards  the  earth,  and  that  it  was  this  constant 
falling  which  prevented  it  from  moving  off  in  a straight 
line.  Newton  then  proceeded  to  prove  by  most 
ingenious  mathematical  reasoning  that  the  force  of 
gravity,  if  it  wrere  such  as  he  supposed  it  to  be,  would 
keep  the  moon  constantly  moving  round  the  earth. 
He  also  showed  that,  if  his  hypothesis  of  gravity  were 


34 


PRIMER  OP  LOGIC. 


[xv 


true,  the  planets  would  move  round  the  sun  as  they 
do.  He  went  on  to  explain  a great  many  peculiarities 
in  the  motions  of  the  planets  and  their  satellites.  He 
showed  that  even  the  comets  though  they  come  and  go 
in  so  apparently  irregular  a manner,  really  move  in  long 
orbits  as  gravity  would  make  them  move.  The  tides, 
too,  are  another  peculiar  effect  of  the  same  force.  Thus 
his  law  became  a verified  hypothesis,  one  so  entirely 
agreeing  with  facts  that  we  cannot  but  believe  it  to 
be  correct.  It  becomes  an  established  law  of 
nature,  and  is  sometimes  called  a theory,  but  this 
last  word,  theory,  is  used  with  several  different  mean- 
ings, and  we  should  take  care  not  to  be  misled  by  it. 
Here  it  means  only  a well-verified  hypothesis. 

125.  Sometimes  it  will  happen  that  two  or  even 
three  quite  different  hypotheses  all  seem  to  agree 
with  certain  facts,  so  that  we  are  puzzled  which  to 
select.  A little  before  Newton  formed  his  hypothesis 
of  gravity,  the  celebrated  Descartes  had  also  formed 
an  hypothesis  to  explain  the  motions  of  the  heavenly 
bodies.  He  suggested  that  they  were  carried  round 
in  kinds  of  large  whirlpools  called  vortices,  and  he 
pointed  out  that  all  the  planets  go  round  the  sun 
in  the  same  direction,  as  they  would  do  in  a whirl- 
pool. The  satellites  of  Jupiter,  then  lately  discovered 
by  Galileo,  also  seemed  to  go  round  Jupiter  in  a small 
whirlpool,  so  that  the  hypothesis  was  held  by  many 
philosopners  of  the  time  to  be  a very  good  one. 
Newton’s  hypothesis  of  gravity,  however,  explained 
the  same  facts,  and  it  was  difficult  to  decide  which 
was  the  best  hypothesis.  That  of  Descartes  was  much 
more  simple  and  easy  to  understand;  that  of  Newton 
explained  a great  many  more  facts  and  in  a more 
exact  manner. 

When  there  are  thus  two  hypotheses,  one  as  good 
as  the  other,  we  need  to  discover  some  fact  or  thing 
which  will  agree  with  one  hypothesis  and  not  with 


XVI.] 


INDUCTIVE  REASONING. 


35 


the  other,  because  this  immediately  enables  us  to 
decide  that  the  former  hypothesis  is  true  and  the 
latter  false.  Newton  pointed  out  that  comets  do  not 
agree  in  their  movements  with  Descartes’  whirlpools, 
because  they  pass  right  through  the  sun’s  great  whirl- 
pool without  moving  like  the  planets  which  rest  in  it. 
Even  when  a comet  passed  through  the  supposed 
smaller  whirlpool  of  Jupiter,  it  moved  on  as  if 
there  were  no  such  whirlpool.  We  now  know,  too, 
that  great  numbers  of  comets  pass  round  the  sun 
in  all  directions.  Each  would  require  its  own  sepa- 
rate whirlpool  according  to  Descartes’  hypothesis, 
but  as  there  can  be  only  one  great  whirlpool  round 
the  sun,  namely,  that  which  carries  the  planets,  it 
becomes  quite  impossible  to  explain  the  motions  of 
the  comets  by  Descartes’  vortices.  All  the  comets 
on  the  other  hand,  as  far  as  they  have  been  observed, 
agree  with  Newton’s  hypothesis  of  gravity. 

126.  When  any  fact,  like  the  motion  of  comets  in 
the  above  case,  enables  us  to  select  one  hypothesis 
and  reject  other  ones,  the  fact  is  called  a Crucial 
Instance,  because  it  serves  like  a Crux  or  Fingerpost, 
to  point  out  the  road  which  we  should  take.  When 
we  try  an  experiment  which  will  decide  in  favour  of 
one  hypothesis  and  against  another,  it  is  called  an 
Experimentum  Crucis. 

XVI.— INDUCTIVE  REASONING  IN  ORDINARY 
LIFE. 

127.  It  is  not  only  in  scientific  matters  that  we  use 
hypotheses  in  order  to  learn,  by  correspondence  with 
facts,  what  has  been  happening.  We  are  continually 
arguing  in  this  way  in  the  commonest  affairs,  and  the 
mind  often  goes  through  all  the  four  steps  of  prelimi- 
nary observation,  hypothesis,  deduction,  and  verifica- 
tion in  a few  seconds.  For  instance,  in  looking  out 

8 


S6 


PRIMER  OF  LOGIC. 


[xvi. 


of  the  window  into  the  street  of  a town,  I see  that 
the  pavement  is  wet,  instead  of  being  dry  as  it  was 
an  hour  before.  In  all  probability  I at  once  consider 
what  can  have  happened  to  cause  the  change.  I 
form  several  hypotheses : rain  may  have  fallen  ; a 
water-cart  may  have  passed  down  the  street ; the 
turncock  may  have  opened  the  water-pipes  in  the 
neighbourhood.  With  great  rapidity  I draw  deduc- 
tions from  these  hypotheses.  A water-cart  does 
not  usually  water  the  footpaths,  but  rain  would  wet 
the  footpath  on  one  side  at  least.  Glancing  at 
the  footpaths  I see  perhaps  that  they  are  dry.  Rain 
then  is  probably  not  the  Cause ; to  be  more  sure, 
I glance  at  the  sky,  and  if  I find  it  apparently  clear 
of  clouds,  this  agrees  well  with  the  hypothesis  of  a 
water-cart,  and  I should  be  finally  convinced  if  I 
discovered  that  the  wet  portions  of  the  street  ran  in 
broad  parallel  lines  nearly  coinciding  with  the  road- 
way, or  only  slightly  overlapping  the  footway,  in 
the  manner  in  which  water-carts  usually  do  their 
work. 

128.  Inquiries  in  courts  of  justice  are  conducted  on 
exactly  the  same  principles.  A burglary  has  been 
committed,  and  the  police  come  to  examine  the  pre- 
mises. This  is  preliminary  observation.  They  find 
that  the  entrance  has  been  skilfully  effected,  and  at 
once  form  hypotheses  as  to  the  men  supposed  to  be 
burglars  who  are  at  large.  They  further  inquire  as  to 
the  appearance  of  men  seen  going  about  in  the  neigh- 
bourhood on  the  night  in  question.  If  any  suspected 
character  agrees  in  appearance  with  a man  seen,  he  is 
probably  apprehended,  because  the  hypothesis  of  his 
guilt  has  received  some  slight  confirmation.  His  house 
being  searched  is  found  to  contain  a jemmy  and  a 
few  other  tools  which  are  used  in  housebreaking. 
Surely,  then,  he  is  a housebreaker;  but,  if  he  is 
the  one  wanted,  the  “jemmy”  in  question  will  pro- 


XVI.] 


INDUCTIVE  REASONING. 


87 


bably  have  been  used  in  breaking  open  the  doors, 
and  will  have  left  a mark  which  should  exactly  agree 
in  size  and  character  with  the  tool  producing  it.  Here 
is  deductive  reasoning.  The  tool  is  carried  to  the 
house  and  compared  with  any  marks  which  can  be 
found,  and  if  it  agrees  there  is  strong  verification. 

129.  The  Tichborne  trial  was  probably  the  longest 
and  most  careful  inquiry  ever  held  to  decide  between 
two  hypotheses.  One  hypothesis  was  that  a certain  fat 
man,  now  in  Dartmoor  Prison,  is  Sir  Roger  Tichborne ; 
another  that  he  is  identical  with  a butcher  called 
Arthur  Orton.  Many  persons  are  said  still  to  believe 
that  he  is  Sir  Roger,  but  in  that  case  they  can  have  no 
idea  what  logic  or  evidence  is.  Some  people  believe 
that  because  Roger’s  mother  and  some  of  his  brother 
officers  and  friends  recognised  the  Claimant  as  Sir 
Roger,  therefore  he  is  so.  But  many  persons  also 
swore  that  he  was  not,  and  some  persons  swore  that 
he  was  Arthur  Orton.  This  kind  of  evidence  is 
very  uncertain  ; for  the  man  was  in  any  case  very  much 
changed  by  age.  Where  people  disagreed  so  much  in 
opinion,  there  was  but  one  way  of  proceeding  safely, 
namely  to  deduce  a great  many  little  circumstances 
which  ought  to  be  true  of  the  Claimant,  things  he 
should  remember,  things  he  ought  to  have  done,  marks 
which  should  appear  on  his  body,  if  he  were  really 
Tichborne.  We  must  compare  these  with  the  evidence 
brought  forward,  and  as  far  as  possible  we  must  make 
a like  comparison  with  the  other  hypothesis  that  the 
Claimant  is  Arthur  Orton.  The  more  slight  and 
apparently  unimportant  these  circumstances  are,  the 
better  proofs  they  make,  because  it  is  less  likely 
that  an  impostor  would  think  of  them.  Thus,  when 
the  Claimant  wrote  to  Lady  Tichborne  from  Australia, 
he  addressed  her  as  Mama,  whereas  Roger  had  always 
addressed  her  in  letters  as  Mother,  and  it  is  against  all 
custom  and  probability  for  a man  as  he  grows  older  to 


ss 


PRIMER  OF  LOGIC. 


[xvi. 


substitute  Mama  for  Mother.  He  was  unacquainted  at 
first  with  many  things  which  a man  could  rarely  forget, 
such  as  the  exact  name  of  his  own  mother,  the  number 
of  his  regiment,  the  name  of  the  vessel  in  which  he 
left  England.  He  was  entirely  ignorant  of  French, 
though  Roger  was  brought  up  in  France  ; yet  he  knew 
some  Spanish,  picked  up  during  a short  residence  in 
South  America.  Roger  had  been  taught  Latin  at 
Stonyhurst,  but  the  Claimant  did  not  know  the  differ- 
ence between  Latin  and  Greek. 

130.  On  the  other  hand  there  were  many  slight 
circumstances  which  agreed  with  the  hypothesis  that 
the  Claimant  was  Orton.  He  said  he  had  suffered 
from  St.  Vitus’  dance,  which  was  true  of  Orton  but 
not  of  Tichborne.  In  his  will  and  journal  he  men- 
tions people  known  to  the  Ortons  but  wholly  unknown 
to  the  Tichborne  family,  and  moreover  displays  entire 
ignorance  of  his  own  Tichborne  property.  The  name 
of  the  ship  in  which  he  says  he  left  England  was  the 
Jessie  Miller , a ship  in  which  it  was  proved  that 
Orton  had  sailed.  And  when  the  Claimant  reached 
England  he  went  straight  to  Wapping  and  inquired 
after  the  old  butcher  who  formerly  lived  there.  It  is 
impossible,  however,  to  give  in  a few  words  any  idea 
of  the  force  of  the  evidence  taken  in  the  Tichborne 
trial,  because  this  force  arose  from  the  immense  number 
of  slight  facts  and  coincidences,  each  of  little  import- 
ance in  itself,  but  all  collectively  making  the  proof  as 
good  as  certain.  A fibre  of  hemp  will  bear  only  a 
small  weight ; but  if  we  twist  many  fibres  into  each 
strand,  and  unite  many  strands  into  a rope,  we  can 
make  a cable  as  strong  as  we  like.  So,  we  can  verify 
an  hypothesis  as  completely  as  any  one  can  desire  if 
we  can  show  that  it  agrees  with  a great  number  of 
diverse  facts. 


XVII.]  OBSERVATION  AND  EXPERIMENT.  89 


XVII.— OBSERVATION  AND  EXPERIMENT. 

13 1.  There  are  commonly  said  to  be  two  ways  in 
which  we  gain  knowledge  of  the  things  around  us. 
The  first  way  is  merely  to  observe  what 
happens  without  our  interference.  We  notice 
the  rise  and  fall  of  the  tides,  and  if  we  remember,  or 
set  down  on  paper,  the  times  at  which  the  tide  is 
highest  on  several  days  in  succession,  we  shall  learn 
that  high  tide  is  about  three  quarters  of  an  hour  later 
on  each  day  than  on  the  previous  day.  If  we  mark 
the  heights  of  the  tides,  too,  we  shall  ascertain  that 
they  are  greatest  at  the  times  of  new  and  full  moon. 
In  this  and  a great  many  other  cases,  we  cannot  in 
any  way  govern  or  regulate  the  things  which  we  notice. 
The  motions  of  the  stars  and  planets,  the  changes  of 
the  weather,  storms,  earthquakes,  volcanoes,  meteors, 
are  things  which  go  on  quite  beyond  our  control.  In 
inquiring  about  such  things,  then,  we  can  only  employ 
simple  observation. 

132.  When  we  can  manage  it,  we  should  make 
experiments,  that  is,  we  should  put  together  the 
things  of  which  we  wish  to  learn  the  nature,  in  such  a 
way  as  to  show  what  the  action  will  be  under  certain 
known  circumstances.  In  experimenting  we 
interfere  with  things,  and  then  observe  the 
result;  experimentation  is  observation  with 
something  more,  namely  regulation  of  the 
things  whose  behaviour  is  to  be  observed. 
The  advantages  of  experiment  over  mere  observation 
are  of  two  kinds. 

133.  In  the  first  place,  we  shall  generally  know 
much  more  certainly  and  accurately  with  what  we  are 
dealing,  when  we  make  experiments  than  when  we 
simply  observe  natural  events.  A chemist  may  very 


90 


PRIMER  OF  LOGIC. 


[XVII. 


properly  wish  to  learn  the  action  of  carbonic  oxide 
gas  upon  animals  and  men,  when  taken  into  the  lungs. 
If  he  trusted  to  mere  observation,  he  would  have  to 
wait  until  some  animal  went  by  accident  into  a room, 
well,  or  other  place  full  of  the  gas.  This  would  only 
rarely  happen,  and  when  it  did  happen,  we  could 
hardly  be  sure  whether  the  gas  was  really  carbonic 
oxide  gas ; for  it  would  probably  be  mixed  with  much 
carbonic  acid  gas,  which  is  said  to  be  quite  different  in 
its  action  on  living  beings.  By  experiment  we  should 
learn  all  that  we  want  very  quickly,  because  we  might 
fill  a glass  vessel  full  of  the  pure  carbonic  oxide  gas, 
and  put  a small  animal  such  as  a rat  into  it,  and 
observe  the  effects  exactly.  When  so  many  rats  and 
other  animals  are  killed  every  day  for  less  necessary 
purposes,  there  can  be  no  harm  in  a chemist  killing 
one  or  two  rats,  when  he  may  thereby  learn  something 
exceedingly  useful  to  men  and  animals  for  ever  after. 
Carbonic  oxide  gas  might  be  very  valuable  for 
warming  and  lighting  houses  at  small  cost,  and  thus 
saving  the  lives  of  many  persons,  if  it  were  not  apt  to 
do  harm  by  escaping  and  poisoning  people.  We  do 
not  know  how  great  the  risk  is,  but  proper  experiments 
would  soon  show  this. 

134.  Nature  sometimes  seems  to  make  experiments 
for  us.  Near  Naples  there  is  a very  curious  cave, 
called  the  Grotto  del  Cane.  Men  can  walk  safely 
into  it,  but  dogs  when  they  enter  soon  fall  down  and 
die,  unless  quickly  removed.  At  first  sight,  it  might 
appear  as  if  there  were  some  substance  in  the  cave 
poisonous  to  dogs,  but  not  to  men.  A few  facts, 
however,  soon  negative  this  hypothesis ; for  if  a 
man  stoop  or  lie  down,  so  as  to  bring  his  mouth 
within  a foot  of  the  floor  of  the  cave,  he  soon  shows 
signs  of  suffocation.  All  that  is  observed  to  happen 
in  the  cave  is  easily  explained  by  the  fact  (Chemistry 
Primer,  Art.  33)  that  carbonic  acid  is  considerably 


xvi  i.  ] OBSER  VA  TION  AND  EXPERIMENT. 


91 


heavier  than  air.  A chemist  can  fill  a glass  jar  with 
this  gas,  and  then  pour  it  into  another  jar,  almost  as  he 
would  pour  water.  A small  animal  put  into  such  a jar 
will  show  signs  of  suffocation  when  the  carbonic  acid 
is  poured  in,  and  this  experiment  completely  explains 
what  is  observed  in  the  Grotto  del  Cane. 

135.  It  is  a further  advantage  of  artificial  experi- 
ments, that,  they  enable  us  to  discover  entirely 
new  substances  and  to  learn  their  properties. 
On  the  surface  of  the  earth,  there  is  always  some 
chemical  action  going  on  among  the  earth,  and  sand, 
and  water,  but  it  is  the  same  as  has  been  going 
on  for  many  thousands  of  years.  It  is  when  we 
choose  particular  substances  and  heat  them,  or  press 
them,  or  electrify  them  in  an  unusual  manner,  that  we 
may  expect  to  meet  something  new.  It  must  have 
been  a surprising  discovery  when  iron  was  first  made 
from  heavy  red  stones  put  into  a hot  charcoal  fire  ; from 
this  and  a series  of  other  experiments,  we  have  gained 
all  that  iron  tools,  iron  vessels,  engines,  railways,  and 
steam-boats  now  do  for  us.  Gold  was  probably 
discovered  by  mere  accidental  observation,  because  it 
is  in  many  places  found  among  the  sands  of  rivers. 
But  mere  observation  could  never  have  led  us  to 
expect  that  from  dull  clay  we  could  get  a beautiful, 
strong,  and  very  light  metal,  named  aluminium.  It 
is  quite  possible  that  careful  and  persevering  experi- 
ments will  some  day  lead  to  the  discovery  of  an 
alloy  of  aluminium,  or  of  some  metal  now  rare 
or  unknown,  which  will  be  more  useful  than  all  our 
gold  and  silver.  We  must  not  suppose  that  we  have 
yet  found  out  the  thousandth  part  of  the  wonderful 
things  which  may  be  in  time  discovered  by  truly 
scientific  reasoning  and  experiment. 


92 


PRIMER  OF  LOGIC. 


[XVIII. 


XVIII.— ANTECEDENTS  AND  CAUSES  OF 
EVENTS. 

136.  What  we  want  to  do,  both  in  observing  and 
experimenting,  is  to  discover  the  exact  circum- 
stances in  which  an  event  will  happen.  In 
other  words,  we  want  to  know  what  things  must  be 
present  in  order  that  something  else  shall  appear. 
All  the  objects  which  are  put  together  in  making  an 
experiment,  or  all  the  circumstances  which  precede 
some  natural  event,  such  as  a thunder-storm,  may  be 
called  antecedents,  or  the  things  going  before. 
All  that  happens  or  is  produced  afterwards  are  called 
consequents.  In  the  case  of  the  thunder-storm, 
warm  moist  air,  a bright  sun,  lofty  swelling  clouds, 
and  a fall  of  the  barometer,  are  usually  the  antecedents, 
and  a heavy  shower  of  rain,  lightning,  thunder,  a 
squall  of  cool  wind,  and  a rise  of  the  barometer,  are 
consequents.  But  it  is  not  to  be  supposed  that  all 
the  antecedents  of  an  event  will  be  necessary  for  its 
production.  The  sun  might  often  be  shining  brightly 
before  a thunder-storm,  but  sometimes  such  storms 
happen  in  the  middle  of  the  night.  The  sun,  therefore, 
seems  not  to  be  needed  to  produce  the  storm.  If  a 
person  be  taken  ill  after  eating  dinner,  all  the  meats 
and  drinks — beef,  potatoes,  cabbages,  bread,  mustard, 
pepper,  salt,  water,  beer,  wine,  or  whatever  else  he 
may  have  taken — will  be  antecedents,  and  his  illness  is 
one  of  the  consequents.  But  it  is  exceedingly  unlikely 
that  there  would  have  been  something  poisonous  in 
each  of  the  dishes  and  drinks.  What  we  shall  need 
to  do  in  such  a case  is  to  find  out  in  what  particular 
substance  the  poison  was  contained,  which  was  the 
necessary  antecedent,  or,  as  it  is  usually  called,  the 
cause  of  his  illness. 

137.  The  cause  of  an  event  is  that  antece- 
dent, or  set  of  antecedents,  from  which  the 


XVIII.] 


ANTECEDENTS  AND  CAUSES. 


93 


event  always  follows.  People  often  make  much 
difficulty  about  understanding  what  the  cause  of  an 
event  means,  but  it  really  means  nothing  beyond  the 
things  which  must  exist  before  in  order  that 
the  event  shall  happen  afterwards.  Sometimes 
it  may  seem  as  if  one  single  antecedent  is  the  sufficient 
cause.  If  there  be  copper  in  the  pickles  eaten  at  a 
meal,  it  may  seem  to  be  the  sole  cause  of  the  illness  of 
the  eater.  But  the  peculiar  formation  of  the  stomach, 
which  becomes  deranged  by  the  presence  of  copper, 
is  also  a necessary  antecedent.  Copper  does  not 
poison  us  when  we  merely  go  near  it.  A single  spark 
may  seem  to  be  the  cause  of  the  explosion  of  a barrel 
of  gunpowder ; but  then  the  gunpowder  is  equally  the 
cause  of  explosion,  and  several  substances  are  requisite 
to  make  gunpowder.  We  shall  in  vain  attempt  to 
produce  an  explosion  with  charcoal,  or  saltpetre,  or 
sulphur  taken  separately.  But  if  we  grind  them  all 
up  together  in  particular  proportions,  and  make  the 
mixture  into  grains,  weget  somethingwhichwill  explode, 
that  is,  very  rapidly  burn,  when  a spark  falls  upon  it. 
Thus  the  sulphur,  the  saltpetre,  the  charcoal,  the 
particular  form  of  the  grains,  the  spark,  and,  it  may  be 
added,  the  absence  of  moisture,  are  all  necessary 
antecedents  or  causes  of  the  explosion. 

138.  The  great  rule  in  making  experiments 
is  to  vary  one  thing  at  a time.  Our  purpose  is 
to  ascertain  exactly  which  antecedents  of  an  event 
are  requisite  to  produce  it.  But  if  I alter  two  or  more 
antecedents  at  the  same  time,  and  the  result  is  altered, 
I cannot  tell  whether  the  change  is  due  to  one  ante- 
cedent, or  to  the  other,  or,  it  may  be,  to  both.  If  a cup 
of  tea  does  not  taste  well,  it  may  be  due  either  to  the 
poor  quality  of  the  tea,  or  to  the  water  not  boiling  when 
it  was  made.  If  I have  a new  pot  of  tea  made  with 
boiling  water  and  a different  kind  of  tea,  I may  get  a 
bettef  cup  of  tea,  but  I shall  not  learn  why  the  former 


94 


PRIMER  OF  LOGIC. 


[XVIII. 


cup  was  bad.  I must  first  try  the  original  kind  of  tea 
with  boiling  water,  and  if  it  still  tastes  bad,  I shall  know 
that  the  fault  was  in  the  tea. 

If  a person  in  perfect  health  falls  down  stairs,  and 
receives  severe  injuries,  followed  by  death,  we  feel 
sure  that  the  fall  caused  the  death.  But  if  a person 
is  seized  with  some  kind  of  fit  and  then  falls  down, 
and  dies  soon  after,  the  fatal  result  may  be  due  either 
to  the  fall  or  the  fit,  or  to  both,  and  the  minutest 
inquiry  may  hardly  settle  which  is  the  case. 

139.  Every  one  knows  that  a bright  piece  of  iron 
soon  rusts  when  exposed  to  the  air.  What  are  the 
causes  of  this  rusting  ? If  we  put  a piece  of  bright 
iron  into  a glass  tube,  exhaust  the  air  out  of  it,  and 
seal  the  tube  up,  the  brightness  of  the  metal  will 
remain  undimmed  for  any  length  of  time.  But  air  is  a 
mixture  of  oxygen,  nitrogen,  vapour  of  water,  carbonic 
acid,  and  small  quantities  of  other  substances.  The 
air  always  contains,  too,  a very  slight  quantity  of 
common  salt,  in  small  particles  which  float  about. 
Any  of  these  substances,  then,  may  be  causes  of  the 
rusting  of  iron,  and  to  decide  which  are  the  causes,  it 
is  not  sufficient  to  withdraw  air  altogether,  nor  even  to 
try  pieces  of  iron  with  pure  oxygen,  nitrogen,  and 
vapour  of  water  separately.  It  will  be  found  that  the 
iron  does  not  rust  with  any  of  these  substances  when 
quite  pure.  The  most  instructive  experiment  is  to 
take  common  air  and  remove  all  the  moisture  from  it ; 
iron  will  remain  perfectly  bright  in  such  air,  so  that 
moisture  is  one  of  the  causes  of  rusting.  But 
it  is  not  the  only  cause ; for  in  perfectly  pure  water,  or 
vapour  of  water,  free  from  oxygen  and  carbonic  acid, 
iron  also  remains  bright.  In  a mixture  of  oxygen, 
watery  vapour,  and  carbonic  acid,  such  as  air  would 
be  without  the  nitrogen,  iron  rapidly  rusts.  By  further 
similar  experiments  we  should  be  led  to  conclude  that 
two  substances,  oxygen  and  vapour  of  water,  are 


XIX.] 


DISCOVERY  OF  AGREEMENT. 


95 


necessary  antecedents  of  the  rusting  of  iron,  and  that 
carbonic  acid,  if  not  altogether  necessary,  makes  iron 
rust  much  more  rapidly.  This  instance  shows  that  it 
is  not  always  easy  to  find  out  exactly  which  of  the 
many  antecedents  of  an  effect  are  the  necessary  ante- 
cedents or  causes  of  the  effect. 

XIX.— DISCOVERY  OF  AGREEMENT. 

140.  What  we  want  to  do  both  in  observing  and 
experimenting,  as  we  have  learnt  in  the  last  Article,  is 
to  discover  the  circumstances  which  always  precede 
an  event.  The  first  step  towards  this  discovery  is 
usually  to  try  and  find  out  what  there  is  alike  in  the 
antecedents  of  every  particular  case  when  the  event 
occurred.  Accordingly,  when  we  wish  to  explain  the 
occurrence  of  anything,  we  should  begin  by- 
thinking  of  everything  like  it  that  we  have 
ever  seen  or  heard  of,  and  then  we  should  compare 
these  things  together  carefully,  and  try  to  detect  the 
exact  likenesses  between  them. 

1 4 1.  Suppose  that  we  see  a bright  rainbow  in  the 
sky,  and  want  to  learn  exactly  why  it  occurs  then  and 
not  at  other  times.  We  want  to  know,  in  short,  what 
are  the  causes  of  its  occurrence.  We  must  begin  by 
comparing  together  all  the  occasions  we  can  remember 
when  a rainbow  was  seen.  We  may  observe  that 
whenever  such  a bow  appeared,  rain  was  falling  some- 
where in  the  sky.  As  the  name  implies,  the  rainbow 
always  occurs  on  or  among  rain  drops,  and  no  one 
ever  saw  a rainbow  with  a perfectly  clear  sky.  At  the 
same  time,  clouds  and  rain  must  not  obscure  the  whole 
sky.  The  sun  must  be  shining  while  the  rain  is  falling. 
We  may  easily  remember  that  rainbows  occur  with 
occasional  brief  showers  of  rain,  or  when  a storm  is 
nearly  at  an  end,  and  the  sun  is  beginning  to  shine 
forth  again. 


96 


PRIMER  OF  LOGIC. 


[xix. 


142.  We  ought  not  to  content  ourselves  with 
considering  ordinary  rainbows  only  ; we  should  think 
and  collect  information  about  all  cases  in  which  similar 
coloured  bows,  or  even  similar  colours,  are  produced. 
Lunar  rainbows  are  sometimes  seen,  and  when  seen 
there  is  a bright  full  moon  shining  on  a shower  of  rain. 
Comparing  lunar  with  solar  rainbows,  we  find  that 
the  sun  is  not  requisite,  but  that  any  bright  beam  of 
light  shining  upon  a shower  of  rain  seems  to  be  the 
necessary  antecedent.  Nor  is  rain  falling  from  the 
sky  quite  necessary.  Some  waterfalls— especially  the 
Rjukan  or  Smoking  Foss  in  Norway — throw  up 
clouds  ot  fine  spray  composed  of  minute  particles  of 
water.  If  we  see  the  sun  shining  in  a particular 
direction  upon  such  spray  a bright  bow,  exactly  like  a 
rainbow,  is  discovered.  The  fine  drops-  of  water  from 
a fountain  occasionally  show  fragments  of  a similar  bow. 
In  the  early  morning  the  grass,  and  shrubs,  and  spiders’ 
webs  are  sometimes  covered  with  drops  of  dew,  and  a 
bright  sunbeam  produces  upon  them  a rainbow  turned 
upside  down.  At  sea  the  colours  of  the  rainbow  may 
be  seen  upon  the  spray  as  it  is  driven  above  the  surface 
of  the  sea  by  the  wind  after  a storm. 

Comparing  the  different  occasions  on  which  the 
same  sort  of  bow  is  seen,  we  discover  that  a beam 
of  light  and  particles  of  water,  in  a particular 
position  are  the  necessary  antecedents  or 
causes  of  the  bow  of  colours.  This  is  nearly  all 
that  simple  observation  can  tell  us,  and  it  forms  merely 
the  first  step  of  preliminary  observation. 

143.  It  was  Sir  Isaac  Newton  who  fully  explained 
how  rainbows  are  produced,  and  this  he  did  by  means 
of  hypotheses.  Long  before  his  time,  indeed,  it  was 
remarked  that  colours,  similar  in  their  succession  to 
the  seven  colours  of  the  rainbow,  are  seen  in  sharply 
cut  glass  vessels,  diamonds,  or  other  transparent 
objects.  Roger  Bacon  _ whom  I mentioned  before 


XX.] 


VARIA  TIONS. 


97 


(Art.  no),  had  discovered  the  circumstances  in  which 
a rainbow  appears,  and  had  also  remarked  the 
resemblance  to  the  colours  of  crystals.  Another 
early  experimenter  pointed  out  that  similar  effects 
are  produced  by  a sunbeam  falling  on  a glass  globe 
full  of  water.  But  Newton  did  a great  deal  more ; 
for  he  imagined  the  different  ways  in  which  a ray 
of  light  might  enter  a drop  of  water  and  get  out 
again,  so  as  to  reach  the  observer’s  eye,  after  having 
been  reflected  and  refracted  within  the  drop.  Knowing 
the  laws  of  the  reflection  and  refraction  of  light,  he 
was  able  to  calculate  the  angle  between  the  ray  coming 
out  and  that  going  in,  and  thus  to  decide  the  size  and 
position  of  a rainbow,  with  respect  to  the  sun  and  the 
eye  of  the  observer. 

144.  Measurements  of  rainbows  agreed  with 
Newton’s  calculations  ; but  he  was  not  contented  with 
this  verification  alone.  He  proved  that  a second,  but 
smaller  portion  of  the  light  entering  a drop  of  rain, 
would  come  out  in  a different  direction,  so  as,  when 
bright  enough,  to  form  another  larger  rainbow.  It  is 
well  known  that  a rainbow  when  very  brilliant  is  often 
accompanied  by  a second  fainter  bow,  and  in  this  we 
have  a complete  verification  of  Newton’s  theory.  In 
such  a case  we  can  see  clearly  how  philosophers, 
beginning  with  simple  preliminary  observation, 
gradually  went  through  all  the  steps  mentioned  in 
Article  118,  and,  by  hypothesis,  deduction,  and  verifi- 
cation, arrived  at  a true  theory. 

XX.— THINGS  WHICH  VARY  IN  QUANTITY. 

145.  The  causes  and  effects  with  which  we  have  to 
deal  in  science  can  often  be  made  to  vary  in  quantity. 
We  can  make  a body  more  or  less  hot  or  cold  ; we  can 
put  a greater  or  less  weight  to  press  upon  it ; or  we  can 
try  how  much  a magnet  of  greater  or  less  force  will 

9 


98 


PRIMER  OF  LOGIC. 


[xx. 


attract  it.  Whenever  we  can  thus  alter  the  quantity  ot 
the  things  experimented  on,  we  can  apply  a rule  for 
discovering  which  are  causes  and  which  are  effects. 
We  must  vary  the  quantity  of  one  thing, 
making  it  at  one  time  greater  and  at  another 
time  less,  and  if  we  observe  any  other  thing 
which  varies  just  at  the  same  times,  it  will 
in  all  probability  be  an  effect. 

We  may  easily  observe,  for  instance,  that  when  air 
is  forced  into  a fire  by  use  of  the  bellows,  greater  heat 
is  produced  ; the  more  powerfully  we  blow,  the  hotter 
the  fire  becomes, _ and  as  soon  as  we  leave  off  blowing, 
the  fire  begins  to  cool.  There  can  be  no  doubt,  then, 
that  a supply  of  air  is  one  of  the  causes  of  the  com- 
bustion of  fuel.  In  the  same  way  we  may  easily  prove 
that  sunlight  is  one  necessary  condition  of  the  growth 
of  plants.  The  sun  partly  makes  the  experiment  for 
us  in  this  case,  because  it  shines  so  much  more 
powerfully,  and  for  a longer  time,  in  summer,  than  in 
winter,  and  we  see  that  grass  and  plants  grow  rapidly 
in  June  and  July,  and  hardly  at  all  in  December  and 
January.  But  this  is  not  quite  satisfactory,  because 
the  air  is  much  warmer  in  summer  than  in  winter,  and 
this  might  perhaps  be  the  reason. 

To  satisfy  ourselves,  we  ought  to  make  more  exact 
experiments,  by  taking  several  plants  of  exactly  the 
same  kind,  planted  in  similar  pots  containing  similar 
soil,  putting  some  plants  where  they  will  receive  bright 
sunshine,  others  where  they  will  be  partially  shaded, 
as  under  trees,  and  some  again  under  boxes  or  in 
sheds,  where  they  will  have  little  or  no  light,  but  where 
the  air  will  be  of  the  same  temperature  as  outside. 
Then,  as  nearly  as  can  be  expected,  the  growth  of  the 
plants  will  be  found  to  correspond  to  the  quantity  ot 
sunshine  falling  upon  them. 

146.  From  the  foregoing  example  we  may  learn  the 
need  of  the  precaution,  to  vary  only  one  thing  at 


XXI.] 


VARIATIONS. 


99 


a time,  as  far  as  we  can  possibly  manage  it.  This  is, 
in  fact,  the  same  precaution  which  we  had  to  take  in 
simple  experiments  (Art.  138),  putting  one  thing 
in  operation  at  once.  Now  we  must  make  one  cause 
greater  and  less,  keeping  all  the  other  things  which 
are  present  of  the  same  quantity  as  exactly  as  we  can. 
If  we  were  to  put  one  plant  where  it  would  have  both 
more  sunshine  and  more  moisture  than  another 
similar  plant,  we  could  not  be  sure  whether  the 
difference  of  growth  was  due  to  the  difference  of  sun- 
shine, or  to  the  difference  of  moisture.  If  possible 
then  we  should  try  plants  having  equal  quantities  of 
moisture,  and  in  every  other  respect  alike,  with 
different  quantities  of  sunshine.  Then  again,  if  we 
want  to  know  the  effect  of  moisture,  we  should  take 
similar  plants,  similarly  supplied  with  sunshine,  and 
differing  only  in  the  supply  of  moisture. 

XXI.— THINGS  WHICH  VARY  PERIODICALLY. 

147.  The  changes  and  motions  which  things  about 
us  exhibit  are  often  what  we  call  periodic,  that  is, 
they  happen  over  and  over  again  in  a similar  manner 
after  equal  periods  or  intervals  of  time.  Day  and 
night  are  periodic  changes,  for  they  happen  alternately, 
and  one  night  is  nearly  equal  in  length  to  the  pre- 
ceding or  following  night.  But,  as  summer  approaches, 
the  daylight  grows  longer,  and  the  nights  shorter ; 
this  happens  in  almost  exactly  the  same  way  every  year, 
so  that  it  is  also  a periodic  change,  depending  upon 
the  motion  of  the  earth  round  the  sun.  The  tides  also 
rising  twice  a day  are  periodic. 

148.  When  things  thus  vary  regularly  and  frequently, 
there  is  a simple  rule,  by  following  which  we  can 
judge  whether  changes  are  connected  together  as 
causes  and  events.  Those  things  which  change 
in  exactly  equal  times  are  in  all  likelihood 


ICO 


PRIMER  OF  LOGIC. 


[xxi. 


connected  together.  Almost  every  day  the  air 
becomes  warmer  in  some  degree  during  the  afternoon, 
and  when  we  take  the  average  of  several  weeks  or 
months,  we  find  that  it  is  almost  always  warmest  about 
three  o’clock  in  the  afternoon.  There  can  be  no 
reasonable  doubt,  of  course,  that  this  increase  of  heat 
is  caused  by  the  sun,  which  is  at  its  highest  point  in 
the  heavens  about  twelve  o’clock,  but  continues  to 
warm  the  air  more  than  it  is  cooled,  for  three  hours 
afterwards.  In  the  same  way  the  warmest  day  in  the 
year  is  about  the  21st  July,  and  this  is,  on  the  average, 
at  an  equal  interval  from  the  21st  June,  the  longest  day. 
Even  if  we  did  not  on  other  grounds  know  it  to  be  the 
case,  we  should  infer  that  the  warmth  of  summer  is  due 
to  that  periodic  motion  of  the  earth  round  the  sun,  which 
causes  the  sun  to  shine  longer  and  brighter  during 
summer  than  during  winter. 

149.  In  other  cases  we  learn  from  periodic  changes 
that  most  unexpected  things  are  connected  together.  I 
have  mentioned  the  tides  as  periodic  events  ; now,  as 
the  tides  happen  at  intervals  of  about  i2§  hours, 
whereas  the  sun  goes  round  the  heavens  at  intervals  of 
about  24  hours,  we  cannot  conclude  by  our  rule  that 
the  sun  is  the  cause  of  the  tides  in  question.  We 
have  to  look  out  for  some  other  cause  which  varies,  or 
moves  round  in  i2§  hours.  We  should  not  meet  with 
anything  exactly  answering  this  description  ; but  we 
should  find  that  the  moon  gets  nearly  to  the  same 
place  in  the  heavens  on  successive  evenings  at  intervals 
double  that  named,  or  24I  hours. 

When  the  moon  is  quite  new,  it  is  seen  early  in  the 
afternoon ; but  as  it  grows  older  and  older,  it  rises 
later,  until  at  last  it  is  not  seen  at  all  till  early  morning. 
If,  when  conveniently  seen  in  the  evening,  we  noted 
the  time  of  its  reaching  a certain  position  in  the  heavens 
we  should  find  the  time  to  be  three  quarters  of  an 
hour  later  every  night.  The  tides  are  just  so  much 


XXI.] 


VARIATIONS. 


IOI 


later  also  ; hence  it  becomes  very  probable  that  the 
attraction  of  the  moon  on  the  ocean  is  the  cause  of 
the  tides.  Sir  Isaac  Newton  showed  beyond  all  doubt 
that  this  was  the  case,  and  he  explained  why  there  are 
two  tides  in  the  24!  hours  instead  of  one  tide. 

150.  In  the  last  thirty  or  forty  years  very  curious 
discoveries  have  been  made  about  variations  in  the 
atmospheres  of  the  sun  and  earth.  It  was  well  known 
to  Sir  William  Herschel  and  other  astronomers,  seventy 
years  ago,  that  the  spots  on  the  sun’s  face  are  much 
more  numerous  and  large  in  some  years  than  in  others. 
Careful  observershaving  registered  the  spots  for  many 
years,  discovered  by  degrees  that  the  years  in  which 
the  spots  are  very  numerous,  happen  at  intervals  of 
about  eleven  years.  There  were  a great  many  spots 
in  1837,  in  1848,  in  1859,  and  in  1870,  and  com- 
paratively few  in  the  intermediate  years,  about  1842, 
1853,  and  1864.  It  was  also  noticed  that  those 
wonderful  and  unaccountable  displays  of  light  in  the 
heavens,  called  Auroras,  are  much  more  frequent  and 
grand  in  some  years  than  in  other  years.  Strange  to 
say,  when  there  are  many  sun-spots  there  are  many 
fine  Auroras,  as  in  the  autumn  of  1859,  and  again  in 
1870.  It  is  impossible  to  say  at  the  present  time  how 
spots  in  the  sun  can  cause  Auroras ; but  they  vary 
together  so  regularly  that  there  can  hardly  be  any 
doubt  about  their  being  connected  together. 

There  is  now  reason  to  believe  that  the  typhoons,  or 
great  storms  which  occur  in  parts  of  the  tropical  re- 
gions of  the  earth,  also  depend  upon  the  sun-spots. 
Meteorologists  are  endeavouring  to  discover  whether 
the  comparative  coldness  or  warmth  of  some  years,  or 
the  variations  in  the  quantity  of  rain,  may  not  also 
have  some  connection  with  the  spots  on  the  sun,  but 
we  ought  to  be  very  careful  in  drawing  conclusions 
about  such  uncertain  changes.  Sir  William  Herschel 
thought  that  the  variations  in  the  price  of  corn 


102 


PRIMER  OF  LOGIC. 


[XXII. 


depended  upon  those  of  the  sun-spots,  and  this,  if 
proved,  would  be  a very  interesting  and  important 
discovery.  I have  tried  to  ascertain  whether  it  is  so 
or  not,  but  have  been  unable  to  find  any  evidence  of 
the  truth  of  Sir  W.  Herschel’s  hypothesis. 

XXII,— REASONING  FROM  EXPERIMENTS. 

15 1.  It  would  be  a mistake  to  suppose  that  the 
making  of  an  experiment  is  inductive  reasoning,  and 
gives  us  without  further  trouble  the  laws  of  nature. 
Experiments  only  give  us  the  facts  upon 
which  we  may  afterwards  reason.  If  I wrap 
up  a piece  of  ice  in  a blanket  and,  placing  it  alongside 
of  another  piece  of  ice  not  wrapped  up,  observe  that 
the  latter  rapidly  melts  away,  and  the  former  does  not, 
there  are  only  two  observations  here.  If  I were  to 
draw  the  conclusion  that  a piece  of  ice  wrapped  up  in 
a blanket  always  melts  less  rapidly  than  one  not 
wrapped  up,  this  would  be  a case  of  inductive  reason- 
ing, but  a bad  case,  because  it  would  not  always  hold 
true.  If  the  temperature  of  the  surrounding  air,  and  of 
other  objects,  were  below  the  freezing  point,  neither 
of  the  pieces  of  ice  would  melt. 

152.  Experiments  then  merely  give  facts,  and  it  is 
only  by  careful  reasoning  that  we  can  learn  when  the 
same  facts  will  be  observed  again.  The  general 
rul'e  is  that  the  same  causes  will  produce  the 
same  effects.  Whatever  happens  in  one  case  will 
happen  in  all  like  cases,  provided  that  they  are  really 
like,  and  not  merely  apparently  so.  The  advantage 
of  being  able  to  try  experiments  is  that  we  ascertain 
exactly  what  are  the  antecedents  and  surrounding 
circumstances  of  an  experiment,  and  we  can  vary  these 
so  as  to  find  out  which  are  important  and  which  are 
not.  If  we  wished  to  decide  exactly  in  what  circum- 


XXII.] 


EXPERIMENTS. 


103 


stances  the  melting  of  ice  would  again  be  observed, 
we  should  have  to  mark  the  temperature  of  the  air,  and 
try  the  experiment  over  and  over  again  at  different 
temperatures.  We  should  also  have  to  consider  whether 
the  sun  was  shining,  or  whether  heat  could  reach  the 
ice  from  fires,  or  warm  bodies  in  the  neighbour- 
hood. 

153.  When  we  have  by  repeated  experiments  tried 
the  effect  which  all  the  surrounding  things  might  have 
on  the  result,  we  can  then  reason  with  much  confidence 
as  to  similar  results  in  similar  circumstances.  But  we 
can  never  be  quite  sure  about  the  matter.  It  is 
always  possible  that  we  have  overlooked  the  thing 
which  is  really  necessary  to  the  result  of  the  experiment. 
It  may  be  very  unlikely,  but  it  is  possible.  Now  and 
then  chemists  find  that  some  experiment  which  they 
thought  they  understood  completely,  deceives  them  and 
gives  quite  unexpected  results.  Sometimes  they  can 
afterwards  explain  these  exceptions  and  failures.  They 
may  happen  to  have  met  with  a new  substance  which 
looked  like  another  substance  familiar  to  them,  but 
was  really  different  in  its  properties.  This  is  the  usual 
way  in  which  new  elements  are  discovered. 

154.  In  order  that  we  may,  from  our  observations 
and  experiments,  learn  the  laws  of  nature  and  become 
able  to  foresee  the  future,  we  must  perform  the  process 
of  generalization.  To  generalize  is  to  draw 
a general  law  from  particular  cases,  and  to 
infer  that  what  we  see  to  be  true  of  a few 
things  is  true  of  the  whole  genus  or  class  to 
which  these  things  belong.  It  requires  much 
judgment  and  skill  to  generalize  correctly,  because 
everything  depends  upon  the  number  and  character  of 
the  instances  about  which  we  reason. 


104 


PRIMER  OF  LOGIC. 


[xxm. 


XXIII.— HOW  AND  WHEN  TO  GENERALIZE. 

155.  It  is  very  difficult  to  explain  how  it  is  that  we 
can  ever  reason  from  one  thing  to  a class  of  things  by 
generalization,  when  we  cannot  really  be  sure  that  the 
things  resemble  each  other  in  the  important  points. 
A wine  merchant  generalizes  on  a small  scale,  when 
he  takes  a single  glass  out  of  a pipe  of  wine,  and  infers 
■that  the  quality  of  every  other  glassful  drawn  from  the 
same  pipe  will  resemble  this  particular  glassful.  But 
then  he  knows  that  the  wine  in  the  pipe  has  been  well 
mixed  up,  so  as  to  be  exactly  alike  in  all  parts. 
Similarly  a broker  who  sells  cotton,  corn  or  sugar,  has 
a sample  taken  which  fairly  corresponds  to  the  whole 
of  the  lot  of  goods,  and  the  buyer  takes  the  goods  on 
the  belief  that  the  sample  is  really  a fair  one. 

156.  Who  is  to  say  what  is  a fair  sample  of  things 
in  nature  ? Can  we  say  that,  because  all  the  stones 
observed  by  us  fall  to  the  ground  again  when 
thrown  up,  therefore  all  other  stones  will  do  the 
same  ? If  so,  upon  what  grounds  do  we  argue  ? We 
have  to  get  a general  law  from  particular  facts.  In 
reality  this  can  only  be  done  by  going  through  all  the 
steps  of  inductive  reasoning  as  explained  in  Articles 
1 12  to  1 1 8.  Having  made  certain  observations,  we 
must  frame  hypotheses  as  to  the  circumstances,  or  laws 
from  which  they  proceed.  .Then  we  must  reason 
deductively,  and,  after  verifying  the  deductions  in  as 
many  cases  as  possible,  we  shall  know  how  far  we  can 
trust  similar  deductions  concerning  future  events. 
But  this  long  process  has  been  performed  very  fre- 
quently by  philosophers,  and  it  usually  leads  to  the 
conclusion,  that  things  which  resemble  each 
other  in  several  of  their  properties  will 
probably  resemble  each  other  in  more  pro- 
perties. There  is  no  certainty  in  the  matter, 


XXIII.] 


GENERA  LIZA  TION. 


i°5 


and  as  I have  already  said,  it  is  difficult  to  judge  when 
we  may,  and  when  we  may  not,  safely  infer  from  some 
things  to  others  in  this  simple  way,  without  making  a 
complete  theory  of  the  matter. 

157.  The  only  rule  that  can  be  given  to  assist  us  is 
that  if  things  resemble  each  other  in  a few 
properties  only,  we  must  observe  many  in- 
stances before  inferring  that  these  properties 
will  always  be  joined  together  in  other  cases. 
We  notice  that  stones  when  thrown  into  the  air,  fall 
to  the  ground,  and  the  same  is  true  of  pieces  of  wood, 
metal,  ice,  leaves  of  trees,  feathers,  or  scraps  of  paper ; 
even  spiders’  webs,  and  the  lightest  things  do  the  same 
when  not  prevented  by  wind.  All  these  are  material 
solid  bodies,  and  we  may  observe  that  the  circumstance 
of  falling  to  the  earth  does  not  seem  to  be  connected 
with  the  colour,  size,  shape  or  other  peculiarities  of 
the  things.  The  things,  in  short,  which  fall,  resemble 
each  other  in  no  apparent  circumstances  except  that 
they  do  fall,  and  that  they  are  solid  and  material. 
Further  observations  show  that  liquids  also  fall,  as  in 
the  case  of  rain.  Clouds,  smoke,  steam,  and  dust 
seem  not  to  fall ; but  further  inquiry  shows  that  in  all 
these  cases  the  particles  are  really  falling  as  rapidly  as 
the  air  will  allow  them.  Moreover,  the  air  itself  falls 
very  rapidly,  when  there  is  an  empty  space  or  vacuum 
into  which  it  can  fall.  Thus  we  find  that  even  solidity 
is  not  necessary  to  the  property  of  falling,  but  that  all 
bodies,  which  consist  of  matter  at  all,  also  have  weight. 
These  circumstances  having  been  so  often  joined 
together,  we  are  justified  in  expecting  that  they  will  be 
joined  together  in  all  future  cases  which  we  may  be 
able  to  observe.  We  conclude,  therefore,  that  all 
material  bodies  will  have  the  property  of  falling  in 
the  same  manner  as  the  stones  and  other  things  ob- 
served. In  other  words,  we  learn  the  general  law  that 
all  things  which  resemble  each  other  in  being  material, 


io6 


PRIMER  OF  LOGIC. 


[XXIII. 


will  also  resemble  each  other  in  the  property  of 
falling  towards  the  earth,  when  not  prevented  by  any 
other  force.  This  is  a very  perfect  instance  of 
generalization,  and  the  conclusion  has  been  confirmed 
by  Newton’s  hypothesis  of  gravitation,  and  the  ob- 
servations made  on  the  motions  of  the  heavenly 
bodies. 

158.  As  a second  instance  of  a good  generalization, 
let  us  consider  what  we  can  infer  about  the  bright 
colours  seen  upon  soap  bubbles.  If  we  were  to 
generalize  carelessly,  we  should  perhaps  infer  that  all 
soapy  water  ought  to  show  bright  colours  ; but  on 
examining  the  soapy  water  which  we  used,  we  should 
find  ourselves  wrong.  To  know  when  to  expect 
similar  colours,  we  must  take  every  opportunity  of 
observing  the  same  thing  again.  When  tar  is  spread 
in  a thin  film  over  water,  as  may  sometimes  be  seen 
in  canals  and  docks,  it  also  shows  most  beautiful 
colours  of  the  same  kind.  Now  the  film  of  tar  does 
not  seem  to  resemble  a soap  bubble  in  anything  but 
being  very  thin.  When  a piece  of  thick  glass  is 
cracked,  and  we  examine  the  crack  very  carefully,  we 
shall  often  find  colours  similar  in  appearance,  though 
perhaps  less  brilliant ; and,  if  we  press  two  plates  of 
glass  together,  or  still  better,  press  a nearly  flat  lense 
upon  a piece  of  plate  glass,  colours  are  seen  near  the 
place  where  the  two  pieces  of  glass  touch.  It  is  difficult 
to  say  in  what  way  tar,  soapy  water,  and  cracks  in  glass 
resemble  each  other,  unless  it  occurs  to  us  that  between 
the  two  surfaces  of  the  glass  there  is  a thin  space 
filled  with  air.  The  colours  thus  appear  in  three  cases 
where  light  falls  upon  a very  thin  film  of  substance 
with  two  bright  surfaces  close  together.  Further 
inouiry  would  show  that  this  was  a good  case  for 
generalization,  and  that  any  very  thin  transparent  plate 
upon  which  light  falls,  will  produce  similar  colours. 
When  we  see  such  colours,  then,  we  may  expect  that 


XXIV.] 


REASONING  BY  ANALOGY. 


107 


there  will  be  found  thin  plates  of  substance.  The 
bright  colours  of  mother-of-pearl  arise  in  this  way 
from  the  extreme  thinness  of  the  layers  of  which  the 
shell  is  formed. 


XXIV.— REASONING  BY  ANALOGY. 

159.  At  the  beginning  of  this  Primer,  I described 
the  way  in  which  we  commonly  reason,  from  one 
thing  directly  to  another  (Articles  4 to  6),  as  from  the 
mountains  of  California  to  those  of  New  South  Wales, 
or  from  one  orange  to  another.  This  kind  of  reasoning 
may  be  called  Reasoning  by  Analogy,  and  it  only 
differs  in  degree  from  that  kind  of  reasoning  called 
generalization.  When  many  things  resemble 
each  other  in  a few  properties,  we  argue 
about  them  by  generalization.  When  a few 
things  resemble  each  other  in  many  proper, 
ties,  it  is  a case  of  analogy.  If  only  a very  few 
things  resemble  each  other  in  a few  points,  we  should 
have  no  ground  for  arguing  from  them  to  other  things. 
But  when  there  are  either  a number  of  things  showing 
resemblance,  or  a number  of  properties  in  which  they 
show  resemblance,  then  we  have  some  grounds  for 
inferring  that  the  same  properties  will  be  found  joined 
together  in  other  cases.  The  rule  for  reasoning 
by  analogy  is,  then,  that  if  two  or  more  things 
resemble  each  other  in  many  points,  they 
will  probably  resemble  each  other  also  in 
more  points. 

160.  If  I see  a machine  with  boiler,  cylinder,  air- 
pump,  piston-rod,  crank,  and  other  parts  exactly 
resembling  those  of  a steam-engine,  I do  not  hesitate 
to  call  it  a steam-engine,  to  assert  that  it  has  a piston, 
valves,  and  other  hidden  parts,  like  all  steam-engines. 
It  is  in  the  same  way  that  we  reason  about  the  sub- 


ioS 


PRIMER  OF  LOGIC. 


[XXVI. 


stance  of  which  anything  is  made.  If  a person  offers 
me  a shilling  as  change,  how  can  I be  sure  that  it  is  a 
good  shilling,  and  made  of  silver  ? All  that  I can  do 
is  to  examine  the  coin,  and  observe  whether  it  has  a 
fine  pure  white  lustre  where  the  surface  is  rubbed  : 
whether  there  is  in  other  parts  of  the  surface  the  black 
tarnish  peculiar  to  silver ; whether  the  coin  seems  to 
be  hard,  and  gives  a sharp  ringing  sound  when  thrown 
down.  If  it  has  all  these  characters  and,  moreover, 
has  a good  impression  exactly  like  that  seen  on  other 
shillings  issued  from  the  mint,  then  it  is  doubtless 
made  of  silver,  and  is  a true  shilling,  that  is  to  say,  it 
will  show  all  the  other  properties  of  standard  silver, 
when  examined  in  a manner  suited  for  showing  them. 

1 6 1.  In  spite  of  the  very  distinct  marks  by  which 
we  may  usually  recognise  a silver  coin,  we  know  that 
counterfeit  ones  are  often  made  and  passed  from  one 
person  to  another.  In  these  and  many  other  cases 
reasoning  by  analogy  is  found  to  be  a very 
uncertain  guide.  In  some  cases  unfortunate 
mistakes  are  committed.  Children  are  sometimes 
killed  by  gathering  and  eating  poisonous  berries, 
wrongly  inferring  that  they  can  be  eaten,  because 
other  berries,  of  a somewhat  similar  appearance,  have 
been  found  agreeable  and  harmless.  Poisonous  toad- 
stools are  occasionally  mistaken  for  mushrooms, 
especially  by  people  not  accustomed  to  gather  them. 
In  Norway  mushrooms  are  seldom  seen,  and  are 
not  eaten ; but  when  I once  found  a few  there,  and 
had  them  cooked  at  an  inn,  I was  amused  by  the 
people  of  the  inn,  who  went  and  collected  toadstools 
and  wanted  me  to  eat  them  also.  This  was  clearly  a 
case  of  mistaken  reasoning  by  analogy.  Even  brute 
animals  reason  in  the  same  way  in  some  degree.  The 
beaten  dog  fears  every  stick,  and  there  are  few  dogs 
which  will  not  run  away  when  you  pretend  to  pick  up 
a stone,  even  if  there  be  no  stone  to  pick  up. 


XXIV.] 


REASONING  BY  ANALOGY. 


109 


162.  In  science  a great  deal  is  learnt  by  analogy. 
We  know  that  the  moon  has  mountains,  because  there 
are  marks  on  the  face  of  the  moon,  which  closely 
resemble  the  appearances  which  our  mountains  would 
have  as  seen  from  the  moon.  The  moon’s  moun- 
tains cast  longer  shadows  as  the  sun  is  setting,  and 
shorter  ones  as  it  is  rising,  just  as  it  happens  on  the 
earth’s  surface.  But  the  ancient  astronomers  were 
misled  by  analogy  into  thinking  that  the  flat  dark 
spaces  on  the  moon’s  surface  were  seas ; they  thought 
that  the  moon  would -naturally  have  oceans  and  seas 
of  various  sizes,  like  the  earth.  By  the  use  of  large 
telescopes  we  now  know  that  there  are  no  seas,  rivers, 
or  other  preceptible  bodies  of  water  on  the  moon. 
(Primer  of  Astronomy,  Art.  129.) 

163.  Sometimes  the  analogy  between  things  is  so 
complete  and  exact  that  we  cannot  doubt  it  for  a 
moment.  The  Chinese  have  printed  mathematical 
tables  of  numbers  called  logarithms  ; but  on  examining 
these  tables  they  were  found  to  have  the  same  mistakes 
as  some  English  tables  of  logarithms.  The  analogy 
was  so  complete  that  we  must  believe  the  Chinese 
tables  to  be  copied  from  the  English  ones.  This  is 
the  only  hypothesis  which  can  explain  the  resemblance. 
As  we  walk  over  the  flags  in  a street,  we  may  often 
notice  that  the  surface  is  wavy,  in  a manner  exactly 
resembling  a fine  sandy  sea  beach,  from  which  the 
tide  has  just  receded.  Sometimes  we  may  notice  on 
flagstones  little  pits  or  hollows,  alike  in  form  and  size  to 
the  holes  which  large  drops  of  rain  make  in  a sandy 
surface.  The  tracks  of  insects  also  and  the  foot-prints 
of  birds,  and  other  animals  are  sometimes  seen.  We 
cannot  explain  these  precise  analogies  between  the 
flagstones  and  the  sea  beach,  except  by  supposing  that 
the  flagstones  really  were  formed  of  the  sand  and  mud 
deposited  by  waves  upon  a sea  beach  countless  ages 
ago.  Geologists  continually  argue  by  analogy  in  this 

10 


I IO 


PRIMER  OF  LOGIC. 


[xxiv. 


way  from  what  goes  on  under  their  eyes  in  the  present 
day  to  what  must  have  happened  when  the  hardest 
rocks  were  being  slowly  formed. 

164.  Of  all  the  planets  Mars  seems  to  have  the 
closest  analogy  to  the  earth.  When  carefully  examined 
it  is  found  to  have  darker  portions,  believed  to  be  seas, 
and  lighter  portions  which  are  probably  land.  At 
each  pole  of  the  planet,  too,  is  a white  round  patch  ; 
now  each  of  these  patches,  if  carefully  watched,  is 
found  to  decrease  when  Mars  is  in  such  a position  as 
to  expose  the  spot  to  the  sun’s  rays,  and  to  increase  at 
other  times.  These  white  spots  thus  behave  exactly 
like  the  masses  of  snow  and  ice  at  the  north  and 
south  poles  of  the  earth.  The  analogy  is  so  perfect 
that  we  conclude,  almost  beyond  doubt,  that  Mars  has 
regions  of  ice  and  snow  at  its  poles  like  the  earth. 
(Primer  of  Astronomy,  Art.  162.) 

165.  There  is  no  way  in  which  we  can 
really  assure  ourselves  that  we  are  arguing 
safely  by  analogy.  The  only  rule  that  can  be 
given  is  this,  that  the  more  closely  two  things  resemble 
each  other,  the  more  likely  it  is  that  they  are  the  same 
in  other  respects,  especially  in  points  closely  connected 
with  those  observed.  Not  only  is  it  very  probable 
that  the  spots  on  Mars  are  composed  of  ice  and  snow, 
but  we  may  also  infer  that  Mars  has  an  atmosphere 
with  winds,  clouds,  rain,  and  other  things  very  like 
our  own.  Some  people  argue,  too,  by  analogy  that 
there  are  probably  living  beings  on  Mars  more  or  less 
resembling  the  plants  and  animals  on  the  earth  ; but  it 
is  evident  that  reasoning  on  such  a matter  is  very 
uncertain.  In  order  to  be  clear  about  our  conclusions, 
we  ought  in  fact  never  to  rest  satisfied  with  mere 
analogy,  but  ought  to  try  to  discover  the  general  laws 
governing  the  case. 

166.  In  analogy  we  seem  to  reason  from  one  fact  to 
another  fact  without  troubling  ourselves  either  with 


XXIV.] 


REASONING  BY  ANALOGY. 


1 1 1 


deduction  or  induction.  But  it  is  only  by  a kind  of 
guess  that  we  do  so  ; it  is  not  really  conclusive  reason- 
ing. We  ought  properly  to  ascertain  what  general 
laws  of  nature  are  shown  to  exist  by  the  facts  observed, 
and  then  infer  what  will  happen  according  to  these 
laws.  This  we  can  do  in  the  case  of  the  white  spots 
on  Mars  to  a great  extent.  We  know  very  well  that 
the  rays  of  the  sun  melt  snow  and  ice,  and  we  observe 
exactly  how  in  the  Arctic  regions  these  effects  take 
place.  We  are  therefore  prepared  to  explain  the 
increase  and  decrease  of  the  white  spots  of  Mars  by 
reasoning  deductively.  But  this  does  not  apply  to  the 
supposed  inhabitants  of  Mars.  No  one  has  ever  been 
able  to  discover  bow  living  beings  came  to  exist  on 
the  earth,  and  no  one  can  be  proved  to  have  produced 
a living  creature  out  of  dead  matter.  We  cannot 
therefore  argue  deductively  that  living  beings  would 
be  produced  on  Mars,  because  its  surface  and  atmo- 
sphere are  in  some  ways  like  those  of  the  earth. 

167.  In  other  matters  people  are  continually  led 
into  errors  by  trusting  to  slight  analogies.  A few 
years  ago  it  was  common  to  hear  it  asserted  that  the 
government  would  make  profit  by  sending  telegrams 
at  very  small  charges.  It  has  even  been  said  that  the 
railway  companies  ought  to  carry  passengers  any  dis- 
tance at  the  same  low  charges  which  are  required  for 
letters  and  books.  These  people  point  to  the  Post 
Office  as  an  institution  which  earns  for  the  govern- 
ment a large  profit  although  it  only  charges  a penny 
for  a letter,  and  a halfpenny  for  a card  or  newspaper. 
They  say,  too,  that  as  the  prices  of  the  daily  news- 
papers were  in  past  years  gradually  reduced  from  six- 
pence to  one  penny,  the  proprietors  got  larger  profits. 
Then  by  analogy  they  infer  that  the  same  will  happen 
with  telegraphs  and  railways.  But  this  is  a mere  guess, 
and  a very  bad  one.  They  ought  not  to  be  satisfied 
with  mere  apparent  resemblance,  but  should  inquire 


1 12 


PRIMER  OF  LOGIC. 


[xxv. 


into  the  reasons  why  the  penny  post  and  the  penny 
newspapers  pay  so  well. 

168.  They  would  find,  for  instance,  that  it  is  not  the 
pennies  paid  for  newspapers  which  make  the  profits  of 
the  publishers,  but  the  large  sums  of  money  which  are 
received  for  advertisements.  In  telegraphs  and  rail- 
ways there  is  little  or  no  source  of  profit  analogous  to 
advertisements.  They  would  find,  again,  that  the  Post 
Office  is  very  profitable  to  the  government,  because  a 
postman  can  carry  a great  many  letters  and  cards  at 
the  same  time,  and  can  deliver  a bundle  of  half-a- 
dozen  almost  as  quickly  as  a single  one.  The  Post 
Office,  therefore,  can  usually  do  more  work  without 
employing  more  men,  and  the  more  letters  it  de- 
livers the  greater  is  the  profit.  With  the  telegraphs, 
however,  it  is  quite  different.  A clerk  cannot  telegraph 
a dozen  messages  along  the  wires  at  once,  nor  even 
two  messages.  Each  message  has  to  be  sent  sepa- 
rately and  delivered  generally  by  a messenger  employed 
for  this  single  purpose.  The  more  messages  are  sent 
the  more  clerks  and  messengers  are  needed.  If  the 
charges  were  to  be  made  very  low,  the  government 
would  lose  a great  deal,  instead  of  gaining  as  they 
do  in  the  Post  Office.  We  find  then  that  reasoning 
by  analogy  is  not  to  be  depended  upon,  unless  we 
make  such  an  inquiry  into  the  causes  and  laws  of  the 
things  in  question,  that  we  really  employ  inductive  and 
deductive  reasoning. 


XXV.— FALLACIES. 

169.  In  learning  how  to  do  right  it  is  always  desir- 
able to  be  informed  as  to  the  ways  in  which  we  are 
likely  to  go  wrong.  In  describing  to  a man  the  road 
which  he  should  follow,  we  ought  to  tell  him  not  only 
the  turnings  which  he  is  to  take,  but  also  the  turnings 


XXV.] 


FALLACIES. 


1 13 

which  lie  is  to  avoid.  Similarly  it  is  a useful  part  of 
logic  which  teaches  us  the  ways  and  turnings  by  which 
people  most  commonly  go  astray  in  reasoning. 

170.  Errors  and  mistakes  in  reasoning  are 
called  fallacies,  that  is,  modes  of  reasoning  which 
deceive.  But  we  ought  not  to  confuse  a false  opinion 
with  the  bad  reasoning  by  which  it  is  reached.  The 
word  fallacy  is  in  fact  an  ambiguous  one  (Art.  29). 
In  one  sense  it  is  a fallacy  that  the  moon  governs  the 
weather,  because  long  and  careful  inquiries  have  shown 
that  there  is  no  correspondence  between  the  changes 
of  the  moon  and  the  changes  of  the  weather.  But 
this  is  a fallacious  or  false  opinion  : the  logical  fallacy 
consists  in  the  bad  reasoning  which  has  by  degrees  led 
people  to  believe  in  the  moon’s  power.  On  one  or 
two  occasions  a person  may  notice  a change  of  weather 
on  the  day  of  new  moon,  and  he  thinks  it  so  singular 
that  he  tells  his  neighbours  of  the  fact,  and  they  re- 
member perhaps  to  have  noticed  the  same  thing  once 
or  twice.  But  it  is  bad  reasoning  to  argue  that,  be- 
cause on  a few  occasions  things  happen  one  after  the 
other,  therefore  the  one  is  the  cause  of  the  other. 

■ 1 7 1.  There  are  at  least  twelve  new  moons  in  each 
year,  and  changes  of  the  weather  take  place  in  this 
country  at  least  once  a week  on  the  average.  It  is 
therefore  quite  likely  that  a new  moon  and  a change  of 
the  weather  will  happen  together  now  and  then.  But 
most  people  believe  that  the  moon  affects  the  weather 
not  because  they  have  really  noticed  it  to  be  so,  but  be- 
cause they  have  often  heard  it  said  to  be  so.  This  is 
not  bad  reasoning,  like  that  which  gave  rise  to  the 
false  belief,  but  it  is  simply  repeating  the  same  false 
opinion.  In  logic  we  ought  to  use  the  word  fallacy  to 
mean  only  false  reasoning,  and  not  false  beliefs. 

172.  Taking  the  word  fallacy,  then,  to  mean  bad 
reasoning,  we  must  remember  that  several  different 
ways  of  falling  into  erroneous  reasoning  were  described 


1 14 


PRIMER  OF  LOGIC. 


[XXVI. 


in  the  Articles  on  deductive  logic.  Whenever  we 
break  the  rules  for  converting  propositions,  the  rules 
of  the  syllogism,  or  any  of  the  other  rules  which  were 
given  for  guiding  us  in  making  inferences,  we  commit 
a fallacy.  If  we  infer  that,  because  all  the  ordinary 
animals  known  to  us  have  the  power  of  moving  them- 
selves, therefore  this  object  which  has  the  power  of 
moving  itself  is  an  animal,  this  is  against  the  third  rule 
of  the  syllogism,  and  is  a case  of  the  fallacy  of  undis- 
tributed middle  term  (Art.  85).  Each  of  the  other 
rules  of  the  syllogism,  when  broken,  gives  rise  to  a 
distinct  kind  of  fallacy  : a breach  of  the  first  rule  is 
called  a Fallacy  of  Four  Terms  : if  we  attempt  to 
draw  a conclusion  from  two  negative  premises,  there  is 
said  to  be  a Fallacy  of  Negative  Premises.  In  these 
and  some  other  cases  the  badness  of  the  reasoning 
ought  to  be  apparent  to  any  one  who  has  carefully 
studied  what  I have  said  about  the  syllogism.  But  an 
argument  may  seem  to  agree  with  the  rules  given  and 
yet  may  be  fallacious,  owing  to  some  confusion  in  the 
meaning  of  the  terms  or  propositions.  We  must  con- 
sider in  what  ways  such  fallacies  are  most  likely  to 
arise. 


XXVI.— FALLACIES  OF  AMBIGUITY. 

173.  Perhaps  the  most  common  cause  of  bad  reason- 
ing is  the  use  of  ambiguous  terms,  which  mean 
one  thing  in  one  place  and  another  thing  elsewhere. 
A word  with  two  distinct  meanings  is  really 
two  words.  If  a person  were  to  argue  that  his  ail- 
ment is  a cold,  and  that  all  cold  is  dispelled  by  heat, 
therefore  his  cold  will  be  dispelled  by  heat,  it  would 
be  absurd  thus  to  confuse  together  a cold  or  catarrh 
with  the  absence  of  heat.  To  argue  thus  is  as  bad  as 
having  four  terms  in  the  same  syllogism,  and  comes 


XXVI.  ] 


FALLACIES. 


”5 

in  fact  to  the  same  thing.  But  in  many  cases  it  is  by- 
no  means  easy  to  see  that  we  are  using  the  same  word 
with  two  meanings. 

174.  It  has  recently  been  argued  that  since  all  men- 
dicants can  be  punished  by  law,  and  Sisters  of  Charity 
who  ask  for  subscriptions  are  mendicants,  therefore 
Sisters  of  Charity  who  ask  for  subscriptions  can  be 
punished.  On  the  same  grounds,  however,  anyone 
who  goes  about  soliciting  subscriptions  for  a charitable 
purpose,  would  be  liable  to  be  sent  to  gaol  as  a rogue 
and  vagabond.  A mendicant  is  no  doubt  one  who 
begs  ; but  we  must  not  convert  this  proposition  simply, 
and  say  that  whoever  begs  is  a mendicant.  A true 
mendicant  not  only  begs,  but  lives  upon  what  he  gets 
by  begging,  and  does  no  useful  work  in  return.  When, 
therefore,  the  law  punishes  mendicancy,  we  must  take 
care  that  it  is  applied  only  to  those  who  beg  for  their 
own  support,  and  make  themselves  a nuisance  to  the 
public.  Lawsuits  frequently  arise  from  the  difficulty 
of  deciding  exactly  what  words  mean.  A kind  of  dull 
black  sbaly  rock  has  in  late  years  become  very  valuable 
because  it  can  be  used  to  make  petroleum.  Some  of 
this  mineral,  known  as  the  Boghead  coal,  having  been 
found  in  an  estate  in  Scotland,  a great  lawsuit  took 
place  to  decide  whether  it  was  or  was  not  really  coal. 
The  uncertain  meaning  of  a word  may  sometimes  be  the 
cause  of  war  between  great  nations.  The  long  dispute 
between  the  United  States  and  England,  about  what  was 
called  the  Alabama  Case,  turned  on  the  meaning  of  the 
expression  “ to  equip  a ship  of  war.”  International 
law  allowed  the  building  and  selling  of  ships  of  war, 
provided  that  they  were  not  sent  out  fully  equipped 
for  fighting  ; but  there  were  differences  of  opinion  as 
to  what  equipping  meant. 

175.  At  the  time  of  the  French  Revolution  some 
philosophers  argued  that  kings  and  rulers  ought  to  do 
exactly  what  the  people  like,  because  they  are  the 


ii6 


PRIMER  OF  LOGIC. 


[XXVI. 


“ servants  of  the  people,”  and  servants  should  obey 
their  masters.  But  here  is  an  obvious  fallacy  of  am- 
biguity. Kings  and  rulers  ought,  no  doubt,  to  serve 
their  people,  in  the  sense  of  doing  what  is  on  the  whole 
most  beneficial  to  the  people.  But  there  is  little  or  no 
analogy  between  service  in  this  sense,  and  the  service 
of  footmen,  porters,  and  domestic  servants  generally 
who  are  paid  to  giveaid  to  their  employerswhen  desired. 
People  fall  into  a somewhat  similar  confusion  of  ideas 
when  they  think  that,  because  a member  of  parliament 
is  elected  to  represent  a certain  borough  or  county, 
therefore  he  is  bound  to  vote  according  to  the  wish  of 
the  people  who  elected  him. 

176.  There  are,  indeed,  several  kinds  of  fallacy 
arising  from  ambiguity,  which  may  be  more  or  less 
exactly  distinguished.  Sometimes  the  confusion 
arises  between  a term  in  its  collective  and 
its  general  meaning,  and  I pointed  out  in  'Art.  17, 
the  need  of  bearing  in  mind  the  existence  of  collective 
terms.  It  would  be  obviously  absurd  to  argue  that 
because  all  the  books  in  the  British  Museum  Library 
are  sure  to  give  information  about  King  Alfred,  there- 
fore any  particular  book  will  be  sure  to  give  it.  By 
“ all  the  books  in  the  British  Museum  Library,”  we 
mean  all  taken  together.  There  are  many  other  cases 
where  the  confusion  is  not  so  evident,  and  where  great 
numbers  of  people  are  unable  to  see  the  exact  differ- 
ence. The  absurd  clamour  about  the  Tichborne  trial 
probably  arose  from  people  thinking  that,  because 
almost  any  witness  brought  against  the  claimant  may 
be  mistaken,  therefore  the  whole  of  the  witnesses  taken 
together  may  be  mistaken.  Looking,  again,  to  the 
things  said  and  done  by  the  claimant,  it  can  be  urged, 
that  he  may  have  forgotten  the  French  language;  he 
may  have  forgotten  the  name  of  his  mother ; he  may 
have  mistaken  the  number  of  his  regiment ; he  may 
have  confused  the  name  of  his  ship  with  that  of  another 


FALLACIES. 


117 


XXVI.] 


ship;  and  so  on,  through  the  hundreds  of  facts  brought 
out  at  the  trial.  But  though  a man,  under  the  circum- 
stances, might  have  done  any  of  these  things,  it  is 
exceedingly  unlikely,  and  indeed  quite  incon- 
ceivable, that  he  should  have  done  all  of  them 
together,  had  he  been  really  Sir  Roger  Tichborne. 
It  is  the  collecting  together  of  a great  many  slight  and 
independent  facts,  which  sometimes  makes  circum- 
stantial evidence,  as  it  is  called,  as  complete  a proof 
as  can  be  needed. 

177.  It  may  be  shown  that  members  of  trades-un:ons 
often  fall  into  a fallacy  of  the  same  kind.  They  argue 
that  stone-masons,  by  limiting  the  number  of  appren- 
tices, may  raise  their  own  wages  ; carpenters  can  do 
the  like ; and  also  brickmakers,  engineers,  cotton- 
spinners,  and  so  on  through  the  whole  list  of  trades. 
It  is  quite  true  that  any  one  trade  may  do  so  to 
a certain  extent ; but  it  does  not  follow  that  all  trades 
taken  together  can  do  it,  because  each  trade,  in  thus 
raising  its  own  wages,  tends  to  injure  the  others  in 
some  degree.  We  may  see  in  this  and  many  other 
cases,  that  a logical  distinction,  which  seemed  absurdly 
obvious  when  first  stated,  may  really  be  overlooked  by 
immense  numbers  of  men,  and  the  confusion  gives  rise 
to  very  great  harm. 

178.  It  is  probably  a fallacy  of  this  kind,  too,  which 
leads  persons  to  argue  that  a very  rich  man  ought  to 
give  a handsome  subscription  to  a particular  institution, 
because  he  would  never  feel  the  loss.  It  may  be  quite 
true  that  he  would  never  feel  the  one  subscription 
solicited,  but  exactly  the  same  argument  might  be 
used  in  many  other  cases.  The  richest  person  would 
soon  be  ruined  by  the  great  number  of  demands  which 
could  be  made  on  the  same  grounds.  What  a sub- 
scriber must  look  to  is  not  the  effect  of  each  separate 
subscription,  but  of  the  whole  of  the  subscriptions 
which  may  be  expected  from  him. 


nS 


PRIMER  OF  LOGIC. 


[xxvi. 


179.  We  sometimes  fall  into  the  opposite  fallacy  to 
that  last  described,  and  argue  that,  because  something 
is  true  of  the  whole  of  a group  of  things,  therefore  it 
is  true  of  any  of  those  things.  It  is  the  fallacy  of 
arguing  from  the  collective  to  the  general. 
All  the  soldiers  in  a regiment  may  be  able  to  capture 
a town,  but  it  is  absurd  to  suppose  that  therefore  every 
soldier  in  the  regiment  could  capture  the  town  single- 
handed.  White  sheep  eat  a great  deal  more  than 
black  sheep ; but  that  is  because  there  are  so  many 
more  of  them.  Ministers  sitting  in  Cabinet  Council 
will  probably  come  to  a wise  decision  concerning  an 
important  question  ; but  it  does  not  follow  that  any 
one  of  them  alone  would  come  to  a wise  decision. 

180.  Moral  teachers  are  fond  of  encouraging  us 
with  various  good  proverbs,  such  as  “ Labor  omnia 
vincit.”  It  is  difficult  to  say  exactly  what  is  meant  by 
“ Labour  overcomes  all  things,”  unless  it  be  that  a 
sufficient  amount  of  labour  will  accomplish  any 
practicable  scheme.  But  of  course  it  does  not  follow 
that,  because  a great  collective  amount  of  labour  will 
build  a pyramid,  or  make  a canal,  or  compile  a cyclo- 
paedia, therefore  a single  person’s  individual  labour 
can  do  such  tasks.  The  proverb  has  little  or  no  value, 
because  every  person  can  give  his  own  meaning  to 
“all  things.”  It  is  said  again,  that  “what  man  has 
done,  that  man  can  do.”  As  I am  a man  I might 
infer  logically  from  these  premises,  that  I can  swim 
across  the  Channel  like  Captain  Webb,  or  write  a 
Paradise  Lost  ’like  Milton,  or  discover  a new  way  of 
making  steel  like  Bessemer,  or  conquer  an  empire  like 
Clive.  The  only  way  in  which  the  proverb  is  really 
true  is  that,  among  a collection  of  a great  many  mil- 
lions of  men,  we  can  find  those  who  can  do  all  these 
things.  Proverbs  often  seem  very  wise,  because  they 
are  very  ambiguous. 

iSr.  Other  fallacies  arise,  not  from  the  confusion  in 


XXVI.] 


FALLACIES. 


119 


meaning  of  any  one  term,  but  from  the  uncertain 
meaning  of  a whole  sentence.  There  is  a hu- 
morous way  of  proving  that  a cat  must  have  three 
tails  : Because  any  cat  has  one  tail  more  than  no  cat, 
and  no  cat  has  two  tails,  therefore  any  cat  has  three 
tails.  As  another  instance  of  the  way  in  which  we  can 
put  nonsense  into  the  form  of  an  apparently  good  syl- 
logism, take  the  following:  No  kind  of  spirituous  liquor 
ought  to  be  drunk  in  excess  ; but  water  is  no  kind  of 
spirituous  liquor  : therefore  water  ought  to  be  drunk 
in  excess.  It  seems  as  if  “ no  kind  of  spirituous 
liquor”  made  a good  middle  term;  but  it  is  not  so, 
and  there  are  really  two  negative  premises  from  which 
we  can  conclude  nothing  (Art.  81). 

182.  A common  kind  of  fallacy  with  orators  and 
those  who  have  to  make  the  best  of  a bad  case,  is 
proving  the  wrong  conclusion,  and  leaving 
people  to  imagine,  in  a confused  sort  of  way,  that  the 
case  is  established.  This  was  the  device  of  the  Irish- 
man, who  was  charged  with  theft  on  the  evidence  of 
three  witnesses,  who  had  seen  him  do  it ; he  proposed 
to  call  thirty  witnesses  who  had  not  seen  him  do  it. 
Equally  logical  was  the  defence  of  the  man  who  was 
called  a materialist,  and  who  replied,  “ I am  not  a 
materialist ; I am  a barber.” ' The  officious  friend 
who  gives  advice  is  likely  to  be  reminded  of  the 
proverb  about  preaching  and  practising.  But  even 
a drunkard  may  properly  denounce  the  evils  of 
tippling,  and  there  is  no  direct  connection  between 
the  logical  strength  of  an  argument  and  the  characters 
of  those  who  use  it. 

183.  One  very  dangerous  kind  of  fallacy,  not  much 
noticed  in  books  on  logic,  but  of  somewhat  the  same 
kind  as  the  last  named,  is  the  fallacy  of  supposing 
that  the  failure  of  an  argument  tends  to  prove 
the  opposite  conclusion.  Old  Mr.  Weller,  as  we 
all  know,  had  the  highest  opinion  of  an  “alibi;”  but 


120 


PRIMER  OF  LOGIC. 


[xxvi. 


lawyers  say  that  nothing  turns  a jury  so  much  against 
a prisoner  as  the  breakdown  of  an  attempt  to  prove 
an  alibi.  William  Sykes  being  charged  with  burglary 
at  Bow  at  one  o’clock  in  the  morning,  brings  witnesses 
to  prove  that  he  was  in  Whitechapel  at  that  time  ; but 
in  cross-examination  it  turns  out  that,  at  the  best,  he  is 
proved  to  have  been  at  Whitechapel  at  midnight,  so 
that  he  might  have  been  at  Bow  by  one  o’clock.  The 
jury  are  apt  to  assume  that  therefore  he  was  not  at 
Whitechapel  at  one  o’clock,  but  at  Bow.  Yet,  unless 
deduced  from  something  in  the  character  of  the  wit- 
nesses, or  the  obvious  bad  faith  of  the  attempt,  there 
is  no  logical  force  in  the  inference  whatever. 

184.  No  number  of  failures  in  attempting 
to  prove  a proposition  really  disprove  it. 
There  is  a general  law  of  mechanics  known  under 
the  name  of  the  parallelogram  of  forces,  which  is 
undoubtedly  true.  A great  many  ingenious  philo- 
sophers have  puzzled  their  brains,  and  written  books 
to  prove  it  true,  but  none  of  them  have  succeeded, 
except  by  assuming  some  other  almost  exactly  similar 
proposition  to  be  true,  which  is  begging  the  question, 
Many  well-meaning  men  have  published  illogical  argu- 
ments to  prove  the  existence  of  a God,  and  it  is  for- 
tunate that  their  failures  have  no  logical  effect  upon  the 
truth  of  that  which  they  hoped  to  demonstrate. 

185.  I mentioned  in  the  last  Article  that  several 
philosophers  had  tried  to  prove  a law  of  mechanics, 
but  had  begged  the  question  by  assuming  some  almost 
exactly  similar  proposition  to  be  true  without  proving 
it.  This  fallacy  of  begging  the  question  con- 
sists in  taking  for  granted  that  which  has  to 
be  proved,  and  is  of  great  importance,  because  the 
fallacy  is  very  difficult  to  detect  and  explain,  and 
occurs  in  several  different  ways.  Sometimes  it  arises 
from  giving  a name  to  a thing,  and  then  supposing 
that  we  have  explained  the  thing.  A wise  man,  as 


XXVI.] 


FALLACIES. 


121 


well  as  a child,  may  reasonably  ask,  why  can  we 
see  through  a glass  window?  Nobody  has  yet  been 
able  to  give  a reason  why  glass,  crystal,  and  various 
solid  things  can  be  seen  through,  while  most  solid 
bodies  cannot.  But  we  sometimes  hear  it  said  that  we 
can  see  through  glass,  “because  it  is  transparent. ” This 
is  clearly  begging  the  question  ; to  say  a thing  is  trans- 
parent is  neither  more  nor  less  than  to  say  that  you  can 
see  through  it.  The  French  dramatist  Moliere  ridiculed 
fallacies  of  this  kind  very  cleverly.  The  father  of  a 
dumb  girl  wants  to  know  why  his  daughter  is  dumb. 
“Nothing  is  more  easy  than  to  explain  it;”  says  the 
physician  Ignarelle ; “it  comes  from  her  having  lost 
the  power  of  speech.”  “Yes,  yes,”  objects  the  father, 
“ but  the  cause,  if  you  please,  why  she  has  lost  the 
power  of  speech.”  Ignarelle  is  quite  ready  with  an 
answer.  “ All  our  best  authors  will  tell  you  that  it  is 
the  impeding  of  the  action  of  the  tongue.” 

1 86.  The  most  frequent  way,  perhaps,  in  which  we 
commit  this  kind  of  fallacy  is  to  employ  names  which 
imply  that  we  disapprove  something,  and  then  argue 
that  because  it  is  such  and  such,  it  must  be  condemned. 
When  two  sportsmen  fall  out  in  some  matter  relating 
to  the  subject  of  game,  one  will,  in  all  probability, 
argue  that  the  act  of  the  other  was  unsportsmanlike, 
and  therefore  it  should  not  have  been  done.  Here  is 
to  all  appearance  a correct  syllogism  : — 

No  unsportsmanlike  act  should  be  done ; 

John  Robinson’s  act  was  unsportsmanlike; 

Therefore,  John  Robinson’s  act  should  not  have 
been  done. 

This  is  quite  correct  in  form ; but  it  is  evidently 
the  mere  semblance  of  an  argument.  “Unsports- 
manlike” means  what  a sportsman  should  not  do. 
The  point  to  be  argued  was  whether  the  act  fell 
11 


PRIMER  OF  LOGIC. 


fxxvi. 


within  the  customary  definition  of  what  was  unsports- 
manlike. 

187.  People  who  do  not  like  examinations  are  fond 
of  saying  that  pupils  are  crammed  for  the  purpose  of 
passing  them,  and  then  they  imply  that  the  knowledge 
thus  gained  by  “ cram,”  is  of  little  value.  But  this  is 
very  bad  reasoning,  and  consists  in  falsely  assuming  that 
all  or  most  candidates  for  examinations  are  crammed 
in  the  same  way.  If  a pupil,  being  quite  unable  to 
understand  a proposition  in  Euclid,  learns  it  off  by 
heart,  and  then  writes  it  out  in  the  examination  room, 
as  if  he  knew  what  he  was  writing,  this  is  a bad  case 
of  cram,  and  the  pupil  gets  no  good  beyond  the 
exercise  of  memory.  But  if  the  pupil  works  up  some 
books  of  Euclid,  and  can  answer  questions  on  them 
intelligently,  he  may  have  crammed  them  in  the  sense 
of  doing  it  to  pass  the  examination,  but  he  has  done 
it  in  a totally  different  way.  Even  though  he  forgets 
the  problems  in  a few  months  or  years,  his  mind  will 
have  been  exercised  in  the  best  manner. 

188.  Words  like  “Cram  ” and  “ Unsportsmanlike,” 
which  are  used  in  this  fallacious  way,  have  been  called 
question-begging  epithets,  and  we  should  always 
be  on  our  guard  against  being  misled  by  them.  It  is 
a good  proverb  which  says  “ Give  a dog  a bad  name 
and  hang  him.” 


XXVII.— FALLACIES  IN  INDUCTIVE 
REASONING. 

189.  I have  already  explained  that  the  way  in  which 
people  very  commonly  argue  from  one  particular  case 
to  another  is  a very  faulty  and  inaccurate  mode  of 
reasoning.  It  depends  upon  assuming  that  there  exists 
some  general  resemblance  or  analogy  between  the 
cases,  but  in  a great  majority  of  instances  people 


xxvii.]  FALLACIES.  123 

make  these  inferences  without  taking  the  trouble  to 
ascertain  that  there  are  sufficient  grounds  for  what 
they  do.  People  often  disregard  all  precautions  and 
assume  that  the  medicine  which  suits  one  person  will 
suit  another,  or  that  what  cures  one  disease  will  cure 
another.  There  is  in  all  persons  at  all  ages  a 
tendency  to  hasty  and  false  generalization. 
The  difficulty  is  not  in  making  inferences,  but  in  making 
correct  ones.  The  mind  is  so  framed  that  we  cannot 
help  classing  together  things  which  look  like  each  other. 
The  child  does  this  as  soon  as  it  can  speak  a few 
words ; it  calls  other  men  “ papa  ” as  well  as  its  own 
father,  because  it  has  no  clear  idea  of  resemblances 
and  differences  between  them.  A beaten  dog  fears  a 
stick  even  in  the  hands  of  a person  who  would  never 
think  of  using  it  upon  the  dog.  But  persons  with 
reasoning  powers  vastly  greater  than  those  of  the  child 
or  dog  often  use  them  quite  as  faultily,  and  generalize 
in  a very  rash  and  careless  manner. 

190.  Travellers  sometimes  make  a rapid  journey  by 
railway  through  a foreign  country,  and  then  come 
home  and  write  a book,  as  if  they  knew  all  about  the 
country.  They  judge  of  millions  of  people  by  the 
few  that  they  get  to  know  slightly  in  hotels  or  public 
conveyances.  If  they  are  cheated  by  one  or  two 
people,  they  infer  that  most  of  the  nation  are  dishonest. 
Too  frequently  we  judge  savage  or  partially  civilized 
people  from  unfavourable  specimens,  with  which  alone 
travellers  come  in  contact.  The  savages  living  on  the 
shores  of  some  unexplored  lands,  like  New  Guinea, 
have  probably  been  ill-treated  by  the  crews  of  trading 
vessels.  Hence  they  are  very  unfriendly  to  strangers. 
But  we  ought  not  to  generalize  and  infer,  that  all  the 
inhabitants  of  a large  country  like  New  Guinea  are 
exactly  like  those  on  the  coast.  Up  to  the  present 
time,  foreigners  have  not  been  able  to  travel  safely 
in  China,  and  can  hardly  visit  more  than  Hong  Kong, 


124 


PRIMER  OF  LOGIC. 


[XXVII. 


Shanghai,  Canton,  Hang  Ivow,  and  a few  other  ports. 
We  ought  not  to  suppose  that  the  whole  of  the  vast 
population  of  China  is  like  that  with  which  we  are 
acquainted  in  these  towns. 

1 9 1.  There  is  really  no  good  reasoning  at  all  in 
assuming  that  other  things  or  persons  are  like  those 
which  we  have  seen.  In  getting  a sample  of  wine 
from  a cask,  as  before  explained  (Art.  155),  we  know 
that  it  has  been  well  mixed  up,  and,  if  requisite,  we 
could  mix  it  on  purpose  to  make  the  sample  a fair  one. 
But  we  cannot  mix  up  the  population  of  a kingdom, 
and  therefore  we  must  not  generalize  about  them  un- 
less we  have  seen  so  many  persons,  in  different  places 
and  ranks  of  society,  as  to  render  it  very  probable  that 
we  have  got  samples  of  all  the  principal  kinds.  We 
should  especially  beware  of  judging  about  any  people 
or  place  from  newspaper  reports  of  what  happens. 
As  people  are  most  interested  in  reading  about  strange 
and  serious  events,  such  as  murders,  robberies,  great 
accidents,  riots,  absurd  deeds,  and  so  forth,  we  fre- 
quently hear  about  these  things,  but  not  about  the 
innumerable  peaceful  and  every-day  events  of  life. 
During  the  last  few  years,  the  newspapers  of  Man- 
chester and  Liverpool,  have  drawn  attention  to  the 
savage  way  in  which  Lancashire  men  kick  their  wives 
and  their  friends,  not  to  speak  of  unoffending  strangers. 
Nevertheless,  visitors  from  the  more  polished  southern 
counties  need  not  fear  to  meet  a brutal  kicker  at  every 
street  corner.  Fortunately,  the  kickers  are  still  so 
small  a proportion  of  the  whole  population,  that  we 
should  hardly  know  of  their  existence  but  for  the 
newspapers.  Judging  from  the  contents  of  American 
papers,  especially  as  quoted  in  English  papers,  it  might 
seem  as  if  American  gentlemen  were  constantly  shoot- 
ing their  intimate  acquaintances  in  bar-rooms ; but,  I 
suppose,  a man  may  live  in  America  all  his  life  without 
seeing  a revolver  fired. 


xxvii.]  FALLACIES.  125 

192.  In  this  way  trades-unions  and  societies  of 
working  men  have  been  unfairly  treated.  Because 
some  such  societies  have,  at  one  time  or  another,  em- 
ployed people  to  commit  illegal  acts  to  punish  work- 
men who  broke  the  rules  of  their  union,  it  is  false 
generalization  to  speak  of  all  unions  as  if  they  did 
the  same.  We  cannot  suppose  that  all  working  men, 
or  all  societies  of  working  men,  are  exactly  like  each 
other,  and  it  is  most  unfair  to  judge  them  all  by  the 
few  worst  cases  which  happen  to  be  made  public. 

193.  All  the  instances  described  in  the  last  three 
articles  are  cases  of  false  and  hasty  generalization. 
But  we  may  without  much  difficulty  distinguish  three 
kinds  of  bad  reasoning  of  the  nature  alluded  to. 
Sometimes  we  argue  wrongly  that  what  is  really  true 
of  a great  many  things,  and,  as  a general  rule,  is  also 
true  of  some  special  case  which  does  not  properly 
come  under  the  rule.  We  extend  the  generalization 
too  far.  At  other  times  we  begin  with  that  which  is 
true  only  in  certain  special  cases,  and  then  treat  it  as 
if  it  were  true  of  many  things,  and  as  a general  rule. 
In  the  third  place,  we  sometimes  argue  from  one  case 
which  is  peculiar,  to  another  case  which  is  also  peculiar, 
so  that  there  is  no  connection  or  real  analogy  what- 
ever. These  three  kinds  of  fallacies  we  may  then 
describe  as  (1)  from  the  general  to  the  special  ; 
(2)  from  the  special  to  the  general ; and  (3)  from 
the  special  to  the  special. 

194.  It  is  a general  law  that  all  plants  grow  by  ab- 
sorbing carbon  from  the  air  under  the  influence  of 
sunshine.  If,  therefore,  we  shut  up  a plant  in  a cellar, 
where  no  daylight  can  reach  it,  we  should  find  it  would 
not  grow,  as  a general  rule.  But  we  must  not  apply 
this  general  rule  to  certain  special  cases,  as,  for  instance, 
where  a plant  derives  nourishment  from  a bulb,  or 
tuber;  potatoes,  hyacinths,  Jerusalem  artichokes,  and 
many  like  plants  will  sprout  and  partially  grow  in  the 


126 


PRIMER  OF  LOGIC. 


[XXVII. 


dark.  Toadstools,  mushrooms,  and  other  kinds  of 
fungi,  again,  are  so  different  in  many  respects  from 
flowering  plants,  that  we  should  hesitate  in  applying  to 
them  any  rule  that  has  only  been  learned  from  the 
observation  of  flowering  plants.  A fungus  is,  in 
fact,  capable  of  growing  upon  the  carbon  contained 
in  the  soil,  and  without  the  aid  of  light.  Great  quan- 
tities of  mushrooms  eaten  jn  Paris  are  grown  in 
caves  under  the  town,  and  that  delicate  kind  of  edible 
fungus  called  the  truffle  grows  altogether  under  the  soil. 

195.  In  legal  matters  we  are  frequently  in  danger 
of  applying  a law  to  cases  which  were  not  intended  to 
come  under  it.  Even  when  no  special  exceptions  are 
mentioned  in  laws,  bye-laws,  or  regulations,  it  may  be 
evident  that  such  exceptions  exist.  It  is  a very  neces- 
sary regulation  on  railways  that  no  one  shall  be  allowed 
to  jump  out  of  a carriage  in  motion.  But  it  is  clearly 
understood  that  such  a rule  does  not  apply  to  railway 
guards,  and  other  servants,  who,  by  practice,  can  do 
it  with  much  less  risk  than  other  people,  and  are  often 
obliged  to  do  it.  Even  a passenger  would  not  be 
punished  for  breaking  such  a regulation,  if  he  could 
show  that  there  was  more  danger  in  remaining  within 
the  carriage  than  in  jumping  out,  the  only  object  of 
the  rule  being  to  save  people  from  danger  of  injury. 

196.  Nothing  is  more  clear  in  the  laws  of  England 
than  that  no  Englishman  can  become  a slave,  and  a 
well-known  song  asserts  in  the  most  positive  way  that 
“ Britons  never  shall  be  slaves.”  Yet  the  judges  are 
continually  occupied  in  sending  persons  into  penal 
servitude,  which  is  only  a longer  name  for  slavery. 
The  fact,  of  course,  is  that  the  general  rule  about 
Britons  is  not  intended  to  apply  to  the  exceptional 
case  of  criminal  Britons,  though  we  seldom  think  of 
this  when  repeating  the  popular  words. 

197.  The  next  kind  of  fallacy  mentioned  was  that 
of  wrongly  arguing  from  a special  case  to  a 


XXVII.]  FALLACIES.  127 

general  law.  If  we  were  to  infer  that,  because 
arsenic,  and  strychnine,  and  prussic  acid  produce 
death  when  taken  in  considerable  doses,  they  always 
produce  death,  we  should  be  mistaken,  because  they 
are  frequently  given  as  medicines  in  exceedingly  small 
quantities  and  much  diluted.  A large  number  of  tee- 
totallers want  to  prohibit  the  sale  of  spirituous  liquors 
altogether,  and  the  reason  which  is  sometimes  given  is 
that  alcohol  is  a poison.  It  is  quite  true  that  when  a 
large  quantity  of  strong  alcoholic  spirit  like  rum  or 
whisky,  is  drunk,  it  may  produce  death  like  a strong 
poison,  and  if  taken  frequently  in  too  large  quantities 
it  is  very  injurious.  But  it  is  a fallacy  to  argue  that 
it  is  therefore  “ poisonous  ” when  taken  in  small 
quantities,  and  mixed  with  plenty  of  water.  As  I 
have  already  mentioned  the  most  terrible  poisons 
cease  to  be  poisonous  when  taken  in  sufficiently  small 
doses.  It  is  all  a question  of  degree  and  quantity. 

198.  There  only  remains  to  be  considered  that  third 
kind  of  false  generalization,  which  consists  in  arguing 
from  one  special  case  to  another  special  case,  between 
which  cases  there  is  no  real  connection.  It  would  be 
absurd  to  argue  that  because  a man  when  assaulted  is 
justified  in  knocking  his  assailant  down  in  self-defence, 
if  he  can  do  it,  therefore  one  prize-fighter  is  justified  in 
knocking  down  another.  Each  is  a special  case,  and 
there  is  no  true  analogy  between  them.  The  practice 
of  betting  is  sometimes  defended  on  the  ground  that 
people  are  not  blamed  for  speculating  in  cotton  or  corn. 
Why,  then,  should  not  people  speculate  upon  horse 
races?  The  fact,  however,  is  that  speculation  is  not  to 
be  approved  unless  it  brings  advantages  to  the  public. 
Speculations  in  corn,  cotton,  and  other  goods  do,  on 
the  whole,  bring  advantages,  both  to  the  public  and 
to  those  who  make  the  speculations  with  the  hope  of 
profit.  But  speculation  upon  horse  races  does  not 
bring  any  such  advantages,  and  far  more  injury  is  done 


128 


PRIMER  OF  LOGIC. 


[XXVII. 


to  those  who  lose  by  betting  than  can  be  balanced  by 
the  profits  of  those  who  win. 

199.  It  is  not  difficult  to  see  that  the  fallacy  here 
described  as  arguing  from  one  special  case  to  another 
is  only  a kind  of  fallacy  of  false  analogy  (Art.  167). 
But  it  is  impossible  too  often  to  remind  people  that, 
on  the  one  hand,  all  correct  reasoning  consists 
in  substituting  like  things  for  like  things,  and 
inferring  that  what  is  true  of  one  will  be  true  of  all 
which  are  similar  to  it  in  the  points  of  resemblance 
concerned  in  the  matter.  All  incorrect  reason- 
ing, on  the  other  hand,  consists  in  putting  one 
thing  for  another  when  there  is  not  the  requi- 
site likeness.  It  is  the  purpose  of  the  rules  of 
deductive  and  inductive  logic  to  enable  us  to  judge  as 
far  as  possible  when  we  are  thus  rightly  or  wrongly 
reasoning  from  some  things  to  others. 


THE  END. 


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ASTHONQMYAt.  $orma'k  Ljcky; 
BOTANY:  Da,  J,  D.  HocwckM*  C. 


EUROPE;  E„  A Freeman,.  T>, 
ENG LAN'Q^f  »•  <***%*  M.  A 
GREECE  C.  -A.  Fyffp,  j&.  A • 
ROMEl  'M.  C’KEiGKTON,  M,  A. 

CHARLOl-f'E  Ml': Yo'^ 
rvY:  George  Groy, 


MMARi  »s 
ITEBATURE': 

LATIN  LITERATURE:  Rev. 
PH  I LO  LOGir^Jif  Pfe  M,  §.  ‘ 
GREEK  LITERATURE:. JR 
THE  BIBLE:  jjjggj^  GROTS, 

LETON 


